There is no prohibition as such.
From a Schengen perspective, you are just leaving the space an re-entering again. As long as your migration status is compatible with that (as you mention, a single entry visa would obviously raise issues), it is fine.

Tax refund is a slightly different thing as 1. it applies to (almost) all EU, not just the Schengen states and 2. it is related to the passenger residency (not nationality nor migratory status). Procedures vary between the EU member states but I suppose that where a proof of itinerary is requested, a custom officer would not validate the refund.