You can contact them and request it, but it generally will not be approved without significant reasons - such as the birth of a child. Your COPR's expiry is tied to your medical exam's expiry. Delaying the COPR would mean re-doing medical exams.
You can leave Canada without a PR card, you can't re-enter. If you are staying wherever you are going in June for a good length of time, you can apply for a PR travel document, or have someone courier you the PR card if it is sent to you by then.