diff --git a/common/lib/xmodule/xmodule/combined_open_ended_module.py b/common/lib/xmodule/xmodule/combined_open_ended_module.py
index a23d0ef1f0..5b1a57f20b 100644
--- a/common/lib/xmodule/xmodule/combined_open_ended_module.py
+++ b/common/lib/xmodule/xmodule/combined_open_ended_module.py
@@ -26,6 +26,7 @@ V1_SETTINGS_ATTRIBUTES = [
     "max_to_calibrate",
     "peer_grader_count",
     "required_peer_grading",
+    "peer_grade_finished_submissions_when_none_pending",
 ]
 
 V1_STUDENT_ATTRIBUTES = [
@@ -303,6 +304,14 @@ class CombinedOpenEndedFields(object):
         scope=Scope.settings,
         values={"min": 1, "step": "1", "max": 5}
     )
+    peer_grade_finished_submissions_when_none_pending = Boolean(
+        display_name='Allow "overgrading" of peer submissions',
+        help=("Allow students to peer grade submissions that already have the requisite number of graders, "
+              "but ONLY WHEN all submissions they are eligible to grade already have enough graders.  "
+              "This is intended for use when settings for `Required Peer Grading` > `Peer Graders per Response`"),
+        default=False,
+        scope=Scope.settings,
+    )
     markdown = String(
         help="Markdown source of this module",
         default=textwrap.dedent("""\
diff --git a/common/lib/xmodule/xmodule/open_ended_grading_classes/combined_open_ended_modulev1.py b/common/lib/xmodule/xmodule/open_ended_grading_classes/combined_open_ended_modulev1.py
index 083998b323..45a5379683 100644
--- a/common/lib/xmodule/xmodule/open_ended_grading_classes/combined_open_ended_modulev1.py
+++ b/common/lib/xmodule/xmodule/open_ended_grading_classes/combined_open_ended_modulev1.py
@@ -127,6 +127,9 @@ class CombinedOpenEndedV1Module():
         self.peer_grader_count = instance_state.get('peer_grader_count', 3)
         self.min_to_calibrate = instance_state.get('min_to_calibrate', 3)
         self.max_to_calibrate = instance_state.get('max_to_calibrate', 6)
+        self.peer_grade_finished_submissions_when_none_pending = instance_state.get(
+            'peer_grade_finished_submissions_when_none_pending', False
+        )
 
         due_date = instance_state.get('due', None)
 
@@ -158,6 +161,9 @@ class CombinedOpenEndedV1Module():
                 'peer_grader_count': self.peer_grader_count,
                 'min_to_calibrate': self.min_to_calibrate,
                 'max_to_calibrate': self.max_to_calibrate,
+                'peer_grade_finished_submissions_when_none_pending': (
+                    self.peer_grade_finished_submissions_when_none_pending
+                ),
             }
         }
 
diff --git a/common/lib/xmodule/xmodule/tests/test_combined_open_ended.py b/common/lib/xmodule/xmodule/tests/test_combined_open_ended.py
index 5944910bab..5d11a4924f 100644
--- a/common/lib/xmodule/xmodule/tests/test_combined_open_ended.py
+++ b/common/lib/xmodule/xmodule/tests/test_combined_open_ended.py
@@ -74,6 +74,7 @@ class OpenEndedChildTest(unittest.TestCase):
             'peer_grader_count': 1,
             'min_to_calibrate': 3,
             'max_to_calibrate': 6,
+            'peer_grade_finished_submissions_when_none_pending': False,
         }
     }
     definition = Mock()
@@ -197,6 +198,7 @@ class OpenEndedModuleTest(unittest.TestCase):
             'peer_grader_count': 1,
             'min_to_calibrate': 3,
             'max_to_calibrate': 6,
+            'peer_grade_finished_submissions_when_none_pending': False,
         }
     }
 
diff --git a/common/lib/xmodule/xmodule/tests/test_self_assessment.py b/common/lib/xmodule/xmodule/tests/test_self_assessment.py
index 2dec24daa1..d18d82a089 100644
--- a/common/lib/xmodule/xmodule/tests/test_self_assessment.py
+++ b/common/lib/xmodule/xmodule/tests/test_self_assessment.py
@@ -55,6 +55,7 @@ class SelfAssessmentTest(unittest.TestCase):
                 'peer_grader_count': 1,
                 'min_to_calibrate': 3,
                 'max_to_calibrate': 6,
+                'peer_grade_finished_submissions_when_none_pending': False,
                 }
         }
 
diff --git a/lms/templates/peer_grading/peer_grading.html b/lms/templates/peer_grading/peer_grading.html
index b0dffe8f9d..101e6341f5 100644
--- a/lms/templates/peer_grading/peer_grading.html
+++ b/lms/templates/peer_grading/peer_grading.html
@@ -1,4 +1,17 @@
 <%! from django.utils.translation import ugettext as _ %>
+<%
+nothing_to_grade_message = _(
+"""
+{p_tag}You currently do not having any peer grading to do.  In order to have peer grading to do:
+{ul_tag}
+{li_tag}You need to have submitted a response to a peer grading problem.{end_li_tag}
+{li_tag}The instructor needs to score the essays that are used to help you better understand the grading
+criteria.{end_li_tag}
+{li_tag}There must be submissions that are waiting for grading.{end_li_tag}
+{end_ul_tag}
+{end_p_tag}
+""").format(p_tag="<p>", end_p_tag="</p>", ul_tag="<ul>", end_ul_tag="</ul>", li_tag="<li>", end_li_tag="</li>")
+%>
 <section class="container peer-grading-container">
     <div class="peer-grading" data-ajax-url="${ajax_url}" data-use-single-location="${use_single_location}">
         <div class="error-container">${error_text}</div>
@@ -9,7 +22,7 @@
             % if success:
                 % if len(problem_list) == 0:
                 <div class="message-container">
-                  ${_("You currently do not having any peer grading to do.  In order to have peer grading to do, you need to have submitted a response to a peer grading problem.  The instructor also needs to score the essays that are used to help you better understand the grading criteria.")}
+                  ${nothing_to_grade_message}
                 </div>
                 %else:
                 <div class="problem-list-container">