diff --git a/ci_scripts/update_doc.py b/ci_scripts/update_doc.py
index ab0e979ca..25c5024fa 100644
--- a/ci_scripts/update_doc.py
+++ b/ci_scripts/update_doc.py
@@ -224,8 +224,39 @@ def add_to_packages_file(slug):
     PACKAGES_FILE.write_text("\n".join(header + entries) + "\n")
 
 
-def git_run(*args):
-    subprocess.run(["git", *args], check=True)
+def git_run(*args, check=True):
+    return subprocess.run(["git", *args], check=check)
+
+
+def checkout_shared_branch(branch):
+    """
+    Check out the shared docs branch as a local worktree HEAD, based on
+    origin/<branch> if it already exists, otherwise on origin/main.
+
+    All docs updates are pushed to this single branch, so a run needs to build
+    on whatever is already there rather than starting from main each time.
+    """
+    git_run("fetch", "origin")
+    remote_ref = f"origin/{branch}"
+    exists = git_run("rev-parse", "--verify", "--quiet", remote_ref, check=False).returncode == 0
+    base = remote_ref if exists else "origin/main"
+    git_run("switch", "--force-create", branch, base)
+
+
+def pr_exists(branch):
+    """Return True if an open PR already targets this branch as its head."""
+    out = subprocess.run(
+        [
+            "gh", "pr", "list",
+            "--repo", REPO,
+            "--head", branch,
+            "--state", "open",
+            "--json", "number",
+            "--jq", "length",
+        ],
+        capture_output=True, text=True, check=True,
+    ).stdout.strip()
+    return out.isdigit() and int(out) > 0
 
 
 def configure_git_identity():
@@ -261,24 +292,30 @@ def main():
     patch_dir = find_patch_dir(slug, version)
     comment = render_gpl_sources_comment()
     yaml_path = DOCS_DIR / f"{slug}.yaml"
-    is_new = not yaml_path.exists()
-    old_content = None if is_new else yaml_path.read_text()
 
-    if is_new:
-        new_content = render_new_yaml(slug, source_code, license, version, patch_dir, comment)
-    else:
-        package_data = yaml.safe_load(old_content) or {}
-        new_content = append_version(
-            old_content, package_data, version, license, patch_dir, comment
-        )
-        if new_content is None:
-            print(f"{slug} {version} is already documented; nothing to do")
-            return
+    branch = "github-actions/update-doc"
+    pr_title = "docs: Update projects"
 
-    branch = f"github-actions/{'add' if is_new else 'update'}-doc-for-{slug}"
-    pr_title = f"docs: {'add' if is_new else 'update'} {slug}"
+    def compute_content():
+        """Read the current YAML (if any) and return (is_new, old_content, new_content)."""
+        is_new = not yaml_path.exists()
+        old_content = None if is_new else yaml_path.read_text()
+        if is_new:
+            new_content = render_new_yaml(
+                slug, source_code, license, version, patch_dir, comment
+            )
+        else:
+            package_data = yaml.safe_load(old_content) or {}
+            new_content = append_version(
+                old_content, package_data, version, license, patch_dir, comment
+            )
+        return is_new, old_content, new_content
 
     if DRY_RUN:
+        is_new, old_content, new_content = compute_content()
+        if new_content is None:
+            print(f"{slug} {version} is already documented; nothing to do")
+            return
         print("[dry-run] Not on main branch — no branch, commit, or PR will be created.")
         print(f"[dry-run] Would write {yaml_path}:")
         diff = difflib.unified_diff(
@@ -293,10 +330,17 @@ def main():
         print(f"[dry-run] Would open PR '{pr_title}' from branch '{branch}' against main")
         return
 
-    yaml_path.write_text(new_content)
     configure_git_identity()
+    checkout_shared_branch(branch)
+
+    # Compute the change against the shared branch's contents, so a package
+    # already documented there by an earlier run in this batch is seen.
+    is_new, _old_content, new_content = compute_content()
+    if new_content is None:
+        print(f"{slug} {version} is already documented; nothing to do")
+        return
 
-    git_run("switch", "-c", branch)
+    yaml_path.write_text(new_content)
     git_run("add", str(yaml_path))
 
     if is_new:
@@ -306,18 +350,22 @@ def main():
     else:
         git_run("commit", "-s", "-m", f"docs: update {slug}\n\nAdd version {version}")
 
-    git_run("push", "origin", branch)
+    git_run("push", "origin", f"HEAD:{branch}")
+
+    if pr_exists(branch):
+        print(f"[+] PR already open for branch '{branch}'; pushed update")
+        return
 
     result = subprocess.run(
         [
-            "gh", "pr", "create", "--draft",
+            "gh", "pr", "create",
             "--repo", REPO,
             "--base", "main",
             "--head", branch,
-            "--reviewer", "threexc,justeph",
+            "--reviewer", "threexc,justeph,luhenry",
             "--title", pr_title,
             "--body",
-            "Automatically generated PR to document a newly published wheel. "
+            "Automatically generated PR to document newly published wheels. "
             "Please review it carefully before merging.\n\n"
             "If necessary, force-push this branch.",
         ],