diff --git a/src/Analyser/ExprHandler/BooleanAndHandler.php b/src/Analyser/ExprHandler/BooleanAndHandler.php
index 383b03c7d66..0c59ec4fac0 100644
--- a/src/Analyser/ExprHandler/BooleanAndHandler.php
+++ b/src/Analyser/ExprHandler/BooleanAndHandler.php
@@ -277,8 +277,8 @@ public function processExpr(NodeScopeResolver $nodeScopeResolver, Stmt $stmt, Ex
 			isAlwaysTerminating: $leftResult->isAlwaysTerminating(),
 			throwPoints: array_merge($leftResult->getThrowPoints(), $rightResult->getThrowPoints()),
 			impurePoints: array_merge($leftResult->getImpurePoints(), $rightResult->getImpurePoints()),
-			truthyScopeCallback: static fn (): MutatingScope => $rightResult->getScope()->filterByTruthyValue($expr->right),
-			falseyScopeCallback: static fn (): MutatingScope => $leftMergedWithRightScope->filterByFalseyValue($expr),
+			truthyScopeCallback: fn (): MutatingScope => $this->conditionalExpressionHolderHelper->specifyWholeExpressionType($rightResult->getScope()->filterByTruthyValue($expr->right), $expr, true),
+			falseyScopeCallback: fn (): MutatingScope => $this->conditionalExpressionHolderHelper->specifyWholeExpressionType($leftMergedWithRightScope->filterByFalseyValue($expr), $expr, false),
 		);
 	}
 
diff --git a/src/Analyser/ExprHandler/BooleanOrHandler.php b/src/Analyser/ExprHandler/BooleanOrHandler.php
index d439a2c8082..657d884b932 100644
--- a/src/Analyser/ExprHandler/BooleanOrHandler.php
+++ b/src/Analyser/ExprHandler/BooleanOrHandler.php
@@ -309,8 +309,8 @@ public function processExpr(NodeScopeResolver $nodeScopeResolver, Stmt $stmt, Ex
 			isAlwaysTerminating: $leftResult->isAlwaysTerminating(),
 			throwPoints: array_merge($leftResult->getThrowPoints(), $rightResult->getThrowPoints()),
 			impurePoints: array_merge($leftResult->getImpurePoints(), $rightResult->getImpurePoints()),
-			truthyScopeCallback: static fn (): MutatingScope => $leftMergedWithRightScope->filterByTruthyValue($expr),
-			falseyScopeCallback: static fn (): MutatingScope => $rightResult->getScope()->filterByFalseyValue($expr->right),
+			truthyScopeCallback: fn (): MutatingScope => $this->conditionalExpressionHolderHelper->specifyWholeExpressionType($leftMergedWithRightScope->filterByTruthyValue($expr), $expr, true),
+			falseyScopeCallback: fn (): MutatingScope => $this->conditionalExpressionHolderHelper->specifyWholeExpressionType($rightResult->getScope()->filterByFalseyValue($expr->right), $expr, false),
 		);
 	}
 
diff --git a/src/Analyser/ExprHandler/Helper/ConditionalExpressionHolderHelper.php b/src/Analyser/ExprHandler/Helper/ConditionalExpressionHolderHelper.php
index e8c1008c183..8d5d7c00e08 100644
--- a/src/Analyser/ExprHandler/Helper/ConditionalExpressionHolderHelper.php
+++ b/src/Analyser/ExprHandler/Helper/ConditionalExpressionHolderHelper.php
@@ -15,6 +15,7 @@
 use PHPStan\Analyser\TypeSpecifier;
 use PHPStan\Analyser\TypeSpecifierContext;
 use PHPStan\DependencyInjection\AutowiredService;
+use PHPStan\Type\Constant\ConstantBooleanType;
 use PHPStan\Type\NeverType;
 use PHPStan\Type\TypeCombinator;
 use function array_keys;
@@ -36,6 +37,34 @@ public function __construct(
 	{
 	}
 
+	/**
+	 * Pins the boolean value of a whole `&&`/`||` condition (`true` in the
+	 * truthy branch, `false` in the falsey branch) into a scope and runs the
+	 * conditional-expression resolution against it, without re-narrowing the
+	 * operands.
+	 *
+	 * The single-variable case (`if ($cond) { $x = 1; } if ($cond) { echo $x; }`)
+	 * already works because the narrowed variable is stored in the scope and
+	 * becomes a guard when the branches merge. A compound condition narrows no
+	 * single variable to a definite value, so nothing is left to guard on.
+	 * Pinning the condition expression's boolean value gives the merge a guard
+	 * keyed on the whole condition, and re-running the resolution lets a later
+	 * identical `if` re-derive the same narrowing — all while preserving any
+	 * side effects (e.g. assignments) already baked into the operand-narrowed
+	 * scope.
+	 */
+	public function specifyWholeExpressionType(MutatingScope $scope, Expr $expr, bool $value): MutatingScope
+	{
+		$specifiedTypes = $this->typeSpecifier->create(
+			$expr,
+			new ConstantBooleanType($value),
+			TypeSpecifierContext::createTrue(),
+			$scope,
+		)->setRootExpr($expr);
+
+		return $scope->filterBySpecifiedTypes($specifiedTypes);
+	}
+
 	public function augmentDisjunctionTypes(
 		MutatingScope $scope,
 		MutatingScope $rightScope,
diff --git a/src/Analyser/MutatingScope.php b/src/Analyser/MutatingScope.php
index e02c18b0da3..c0164532acd 100644
--- a/src/Analyser/MutatingScope.php
+++ b/src/Analyser/MutatingScope.php
@@ -3325,6 +3325,33 @@ public function filterByFalseyValue(Expr $expr): self
 		return $scope;
 	}
 
+	/**
+	 * A multi-guard conditional holder may take some of its guards from the
+	 * current scope's already-narrowed expressions (e.g. the `!prevCond` part of
+	 * an `if`/`elseif` chain that is definite in scope but not re-specified by the
+	 * condition currently being applied), as long as at least one of its guards is
+	 * actively specified — so the holder is relevant to that condition rather than
+	 * firing on ambient scope state. Single-guard holders never seed, preserving
+	 * their existing behaviour.
+	 *
+	 * @param array<string, ExpressionTypeHolder> $conditionHolders
+	 * @param array<string, ExpressionTypeHolder> $specifiedExpressions
+	 */
+	private function multiGuardCanSeedFromScope(array $conditionHolders, array $specifiedExpressions): bool
+	{
+		if (count($conditionHolders) < 2) {
+			return false;
+		}
+
+		foreach (array_keys($conditionHolders) as $holderExprString) {
+			if (array_key_exists($holderExprString, $specifiedExpressions)) {
+				return true;
+			}
+		}
+
+		return false;
+	}
+
 	/**
 	 * @return static
 	 */
@@ -3415,13 +3442,25 @@ public function filterBySpecifiedTypes(SpecifiedTypes $specifiedTypes): self
 					) {
 						continue;
 					}
-					foreach ($conditionalExpression->getConditionExpressionTypeHolders() as $holderExprString => $conditionalTypeHolder) {
+					$conditionHolders = $conditionalExpression->getConditionExpressionTypeHolders();
+					$allowSeed = $this->multiGuardCanSeedFromScope($conditionHolders, $specifiedExpressions);
+					foreach ($conditionHolders as $holderExprString => $conditionalTypeHolder) {
 						if (
-							!array_key_exists($holderExprString, $specifiedExpressions)
-							|| !$conditionalTypeHolder->equals($specifiedExpressions[$holderExprString])
+							array_key_exists($holderExprString, $specifiedExpressions)
+							&& $conditionalTypeHolder->equals($specifiedExpressions[$holderExprString])
 						) {
-							continue 2;
+							continue;
+						}
+						if (
+							$allowSeed
+							&& array_key_exists($holderExprString, $scope->expressionTypes)
+							&& $scope->expressionTypes[$holderExprString]->getCertainty()->yes()
+							&& $conditionalTypeHolder->getType()->equals($scope->expressionTypes[$holderExprString]->getType())
+						) {
+							continue;
 						}
+
+						continue 2;
 					}
 
 					$conditions[$conditionalExprString][] = $conditionalExpression;
@@ -3437,14 +3476,26 @@ public function filterBySpecifiedTypes(SpecifiedTypes $specifiedTypes): self
 					if ($conditionalExpression->getTypeHolder()->getCertainty()->no()) {
 						continue;
 					}
-					foreach ($conditionalExpression->getConditionExpressionTypeHolders() as $holderExprString => $conditionalTypeHolder) {
+					$conditionHolders = $conditionalExpression->getConditionExpressionTypeHolders();
+					$allowSeed = $this->multiGuardCanSeedFromScope($conditionHolders, $specifiedExpressions);
+					foreach ($conditionHolders as $holderExprString => $conditionalTypeHolder) {
+						if (
+							array_key_exists($holderExprString, $specifiedExpressions)
+							&& $conditionalTypeHolder->getCertainty()->equals($specifiedExpressions[$holderExprString]->getCertainty())
+							&& $conditionalTypeHolder->getType()->isSuperTypeOf($specifiedExpressions[$holderExprString]->getType())->yes()
+						) {
+							continue;
+						}
 						if (
-							!array_key_exists($holderExprString, $specifiedExpressions)
-							|| !$conditionalTypeHolder->getCertainty()->equals($specifiedExpressions[$holderExprString]->getCertainty())
-							|| !$conditionalTypeHolder->getType()->isSuperTypeOf($specifiedExpressions[$holderExprString]->getType())->yes()
+							$allowSeed
+							&& array_key_exists($holderExprString, $scope->expressionTypes)
+							&& $conditionalTypeHolder->getCertainty()->equals($scope->expressionTypes[$holderExprString]->getCertainty())
+							&& $conditionalTypeHolder->getType()->isSuperTypeOf($scope->expressionTypes[$holderExprString]->getType())->yes()
 						) {
-							continue 2;
+							continue;
 						}
+
+						continue 2;
 					}
 
 					$conditions[$conditionalExprString][] = $conditionalExpression;
@@ -3843,7 +3894,43 @@ private function createConditionalExpressions(
 			$typeGuards[$exprString] = $holder;
 		}
 
-		if (count($typeGuards) === 0) {
+		// Path-condition guards distinguish this branch from the other one along
+		// an `if`/`elseif`/`else` chain. Unlike $typeGuards they keep the branch's
+		// own condition (e.g. the `elseif` operand), which $guardsToExclude drops
+		// because the merge absorbs its narrowed value. A branch reached after one
+		// or more preceding branches were skipped needs *all* of these together
+		// (`!prevCond && thisCond`) as a single guard; any one of them alone would
+		// also match a sibling branch and is dropped when that sibling merges in.
+		// Only pre-existing variables narrowed by the condition qualify — freshly
+		// assigned variables (absent from the other branch) are not conditions.
+		$conditionGuards = [];
+		foreach ($newVariableTypes as $exprString => $holder) {
+			if ($holder->getExpr() instanceof VirtualNode) {
+				continue;
+			}
+			if (!$holder->getCertainty()->yes()) {
+				continue;
+			}
+			if (!array_key_exists($exprString, $mergedExpressionTypes)) {
+				continue;
+			}
+			if (
+				!array_key_exists($exprString, $theirExpressionTypes)
+				|| !$theirExpressionTypes[$exprString]->getCertainty()->yes()
+			) {
+				continue;
+			}
+			if ($mergedExpressionTypes[$exprString]->equalTypes($holder)) {
+				continue;
+			}
+
+			$conditionGuards[$exprString] = $holder;
+		}
+
+		// $typeGuards drives the single-guard holders; $conditionGuards drives the
+		// multi-guard (path-condition) holders. Either may be empty on its own, but
+		// when both are there is nothing to record.
+		if (count($typeGuards) === 0 && count($conditionGuards) < 2) {
 			return $conditionalExpressions;
 		}
 
@@ -3858,6 +3945,27 @@ private function createConditionalExpressions(
 				continue;
 			}
 
+			// Carry a value across the chain only for a plain variable whose
+			// *definedness* the branch establishes (defined here, not in the other
+			// branch). A variable already defined in both branches is a condition
+			// variable, not a branch product, so keying its narrowed value on the
+			// sibling conditions (`if rel=false then document=false`) would be
+			// unsound. Restricting to variables also keeps these path-condition
+			// holders out of the way of the narrowing recorded for compound
+			// boolean operands (e.g. `$x = $a->foo() !== null && ...; if ($x)`).
+			$targetIsConditionVariable = array_key_exists($exprString, $theirExpressionTypes)
+				&& $theirExpressionTypes[$exprString]->getCertainty()->yes()
+				&& $holder->getCertainty()->yes();
+
+			if ($holder->getExpr() instanceof Variable && !$targetIsConditionVariable) {
+				$pathGuards = $conditionGuards;
+				unset($pathGuards[$exprString]);
+				if (count($pathGuards) >= 2) {
+					$conditionalExpression = new ConditionalExpressionHolder($pathGuards, $holder);
+					$conditionalExpressions[$exprString][$conditionalExpression->getKey()] = $conditionalExpression;
+				}
+			}
+
 			$variableTypeGuards = $typeGuards;
 			unset($variableTypeGuards[$exprString]);
 
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14871.php b/tests/PHPStan/Analyser/nsrt/bug-14871.php
new file mode 100644
index 00000000000..1e575bf8b80
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14871.php
@@ -0,0 +1,147 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14871;
+
+use PHPStan\TrinaryLogic;
+use function PHPStan\Testing\assertType;
+use function PHPStan\Testing\assertVariableCertainty;
+
+function logicalOr(bool $cond, bool $f): void
+{
+	if ($cond || $f) {
+		$x = 1;
+	}
+
+	if ($cond || $f) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $x);
+		assertType('1', $x);
+	}
+}
+
+function logicalAnd(bool $cond, bool $f): void
+{
+	if ($cond && $f) {
+		$z = 1;
+	}
+
+	if ($cond && $f) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $z);
+		assertType('1', $z);
+	}
+}
+
+function wordOperators(bool $cond, bool $f): void
+{
+	if ($cond or $f) {
+		$x = 1;
+	}
+
+	if ($cond or $f) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $x);
+	}
+}
+
+function nestedCompound(bool $a, bool $b, bool $c): void
+{
+	if (($a && $b) || $c) {
+		$x = 1;
+	}
+
+	if (($a && $b) || $c) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $x);
+	}
+}
+
+function comparisonOperands(int $a, int $b): void
+{
+	if ($a > 0 || $b > 0) {
+		$x = 1;
+	}
+
+	if ($a > 0 || $b > 0) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $x);
+	}
+}
+
+function typeNarrowingCarried(?int $a, bool $b): void
+{
+	if ($a !== null || $b) {
+		$x = 'set';
+	}
+
+	if ($a !== null || $b) {
+		assertType("'set'", $x);
+	}
+}
+
+// https://phpstan.org/r/aab74e73-2bfe-432b-8bcd-f9b939d2eaab
+// An `if`/`elseif`/`else` chain repeated with identical compound conditions must
+// carry definedness across every branch, not just the first.
+function compoundElseIfChain(bool $rel, bool $document, bool $overwrite): void
+{
+	if ($rel || $overwrite) {
+		$vvv = 1;
+	} elseif ($document) {
+		$aaa = 2;
+	} else {
+		$eee = 3;
+	}
+
+	if ($rel || $overwrite) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $vvv);
+	} elseif ($document) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $aaa);
+	} else {
+		assertVariableCertainty(TrinaryLogic::createYes(), $eee);
+	}
+}
+
+// The same chain with single-variable conditions (a pre-existing limitation for
+// the non-first branches) must work too.
+function singleVarElseIfChain(bool $a, bool $b): void
+{
+	if ($a) {
+		$x = 1;
+	} elseif ($b) {
+		$y = 2;
+	} else {
+		$z = 3;
+	}
+
+	if ($a) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $x);
+	} elseif ($b) {
+		assertVariableCertainty(TrinaryLogic::createYes(), $y);
+	} else {
+		assertVariableCertainty(TrinaryLogic::createYes(), $z);
+	}
+}
+
+// A condition with a side effect in one operand must still narrow correctly
+// after the `if` (the whole-condition pinning must not re-run the assignment).
+function assignmentInOperand(string $foo): int
+{
+	if (!ctype_digit($foo) || ($foo = intval($foo)) < 1) {
+		return -1;
+	}
+
+	assertType('int<1, max>', $foo);
+
+	return $foo;
+}
+
+function unsetBetweenIfs(?int $a, bool $b): void
+{
+	if ($a !== null || $b) {
+		$x = 'set';
+	}
+
+	if (rand(0,1)) {
+		unset($x);
+	}
+
+	if ($a !== null || $b) {
+		assertType("'set'", $x);
+		assertVariableCertainty(TrinaryLogic::createMaybe(), $x);
+	}
+}