diff --git a/Changelog.md b/Changelog.md
index 6196f978c..9258b0d9c 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -12,6 +12,7 @@ Enhancements:
 
 * Improve the IO emulation in the output capture matchers (`output(...).to_stdout` et al)
   by adding `as_tty` and `as_not_tty` to change the `tty?` flags. (Sergio Gil Pérez de la Manga, #1459)
+* Add support for compound output matchers. (Eric Mueller, #1460)
 
 ### 3.13.1 / 2024-06-13
 [Full Changelog](http://github.com/rspec/rspec-expectations/compare/v3.13.0...v3.13.1)
diff --git a/lib/rspec/matchers/built_in/output.rb b/lib/rspec/matchers/built_in/output.rb
index 888ccaee2..503ebaa1f 100644
--- a/lib/rspec/matchers/built_in/output.rb
+++ b/lib/rspec/matchers/built_in/output.rb
@@ -186,6 +186,7 @@ def capture(block)
           captured_stream.string
         ensure
           $stdout = original_stream
+          $stdout.write(captured_stream.string) unless $stdout == STDOUT # rubocop:disable Style/GlobalStdStream
         end
       end
 
@@ -209,6 +210,7 @@ def capture(block)
           captured_stream.string
         ensure
           $stderr = original_stream
+          $stderr.write(captured_stream.string) unless $stderr == STDERR # rubocop:disable Style/GlobalStdStream
         end
       end
 
@@ -223,21 +225,47 @@ def capture(block)
           # thread, fileutils, etc), so it's worth delaying it until this point.
           require 'tempfile'
 
+          # This is.. awkward-looking. But it's written this way because of how
+          # compound matchers work - we essentially need to be able to tell if
+          # we're in an _inner_ matcher, so we can pass the stream-output along
+          # to the outer matcher for further evaluation in that case. Added to
+          # that, it's fairly difficult to _tell_, because the only actual state
+          # we have access to is the stream itself, and in the case of stderr,
+          # that stream is really a RSpec::Support::StdErrSplitter (which is why
+          # we're testing `is_a?(File)` in such an obnoxious way).
+          inner_matcher = stream.to_io.is_a?(File)
+
+          # Careful here - the StdErrSplitter is what is being cloned; we're
+          # relying on the implemented clone method of that class (in
+          # rspec-support) to actually clone the File for ensure-reopen.
           original_stream = stream.clone
+
           captured_stream = Tempfile.new(name)
 
           begin
             captured_stream.sync = true
             stream.reopen(captured_stream)
             block.call
-            captured_stream.rewind
-            captured_stream.read
+            read_contents(captured_stream)
           ensure
+            captured_content = inner_matcher ? read_contents(captured_stream) : nil
             stream.reopen(original_stream)
-            captured_stream.close
-            captured_stream.unlink
+            stream.write(captured_content) if captured_content
+            clean_up_tempfile(captured_stream)
           end
         end
+
+        private
+
+        def read_contents(captured_stream)
+          captured_stream.rewind
+          captured_stream.read
+        end
+
+        def clean_up_tempfile(tempfile)
+          tempfile.close
+          tempfile.unlink
+        end
       end
     end
   end
diff --git a/spec/rspec/matchers/built_in/output_spec.rb b/spec/rspec/matchers/built_in/output_spec.rb
index 3873013d1..68a1b1672 100644
--- a/spec/rspec/matchers/built_in/output_spec.rb
+++ b/spec/rspec/matchers/built_in/output_spec.rb
@@ -139,6 +139,12 @@ def invalid_block
       }.to fail_including("expected block to not output a string starting with \"f\" to #{stream_name}, but output \"foo\"\nDiff")
     end
   end
+
+  context "expect { ... }.to output(matcher1).#{matcher_method}.and output(matcher2).#{matcher_method}" do
+    it "passes if the block outputs lines to #{stream_name} matching both matchers", :pending => RSpec::Support::Ruby.jruby? && matcher_method =~ /any_process/ do
+      expect { print_to_stream "foo_bar" }.to matcher(/foo/).and matcher(/bar/)
+    end
+  end
 end
 
 module RSpec