diff --git a/test/include/problems/SlowProblem.h b/test/include/problems/SlowProblem.h
index b48639899ce7..4b5f46493e80 100644
--- a/test/include/problems/SlowProblem.h
+++ b/test/include/problems/SlowProblem.h
@@ -30,5 +30,6 @@ class SlowProblem : public FEProblem
 
   const std::vector<Real> _seconds_to_sleep;
   const bool _nested_print;
+  const bool _nested_print_end;
   const bool _nested_section;
 };
diff --git a/test/src/problems/SlowProblem.C b/test/src/problems/SlowProblem.C
index a1b54a5025e0..61a59cabc7a6 100644
--- a/test/src/problems/SlowProblem.C
+++ b/test/src/problems/SlowProblem.C
@@ -25,6 +25,9 @@ SlowProblem::validParams()
   // Parameters to print perf graph live print interactions
   params.addParam<bool>(
       "print_during_section", false, "Whether to nest a console print inside the timed section");
+  params.addParam<bool>("print_at_end_of_section",
+                        false,
+                        "Whether to nest a console print right at the end of the timed section");
   params.addParam<bool>(
       "nest_inside_section", false, "Whether to nest another section inside the timed section");
 
@@ -35,6 +38,7 @@ SlowProblem::SlowProblem(const InputParameters & params)
   : FEProblem(params),
     _seconds_to_sleep(getParam<std::vector<Real>>("seconds_to_sleep")),
     _nested_print(getParam<bool>("print_during_section")),
+    _nested_print_end(getParam<bool>("print_at_end_of_section")),
     _nested_section(getParam<bool>("nest_inside_section"))
 {
   if (_seconds_to_sleep.empty())
@@ -52,12 +56,18 @@ SlowProblem::solve(unsigned int nl_sys_num)
       TIME_SECTION("slow", 1, "Testing Slowness");
       std::this_thread::sleep_for(std::chrono::duration<Real>(delay));
     }
-    else if (_nested_print)
+    else if (_nested_print_end)
     {
       TIME_SECTION("slow", 1, "Testing Slowness");
       _console << "Timed section just started, printing something though" << std::endl;
       std::this_thread::sleep_for(std::chrono::duration<Real>(delay));
     }
+    else if (_nested_print)
+    {
+      TIME_SECTION("slow", 1, "Testing Slowness");
+      std::this_thread::sleep_for(std::chrono::duration<Real>(delay));
+      _console << "Timed section is about to finish" << std::endl;
+    }
     else if (_nested_section)
     {
       TIME_SECTION("slow", 1, "Testing Slowness");
@@ -74,6 +84,7 @@ SlowProblem::otherTimedSection() const
 {
   Real delay = getDelay();
   TIME_SECTION("slowish", 2, "Testing Nested Slowness");
+  _console << "Interrupt" << std::endl;
   std::this_thread::sleep_for(std::chrono::duration<Real>(delay));
 }
 
diff --git a/test/tests/utils/perf_graph_live_print/tests b/test/tests/utils/perf_graph_live_print/tests
index 781275010821..0440d375977f 100644
--- a/test/tests/utils/perf_graph_live_print/tests
+++ b/test/tests/utils/perf_graph_live_print/tests
@@ -31,6 +31,17 @@
     design = 'utils/PerfGraphLivePrint.md'
     requirement = 'The system shall be able to display the automatic print-out of a timed section even when an external print happened before the threshold for the automatic print-out was met.'
   []
+  [stats_interrupted_by_regular_print]
+    # this test does not address the warnings 'direct to Moose::out' issue #23750
+    type = RunApp
+    input = perf_graph_live_print.i
+    cli_args = 'Problem/print_at_end_of_section=true'
+    expect_out = "Timed section is about to finish\nFinished"
+
+    issues = '#23746'
+    design = 'utils/PerfGraphLivePrint.md'
+    requirement = 'The system shall be able to display the automatic print-out of a timed section even when an external print happened right at the end of the timed section, before the statistics for the sections were printed.'
+  []
 
   [multiapps]
     type = RunApp