Generally, you can see if a visa is a multi entry visa by looking at the top right corner, where it should say 'MULT' for multiple entries. If that is the case, and as long as your visa is still valid, you can usually leave and re-enter Germany multiple times.
If your current visa is about to expire, but you have/will have handed in the application for your new permit before the expiry date, you can usually get a ‘Fiktionsbescheinigung’. This is a certificate issued by the immigration office serving as official proof that your visa is still valid while the new application is being processed. Please be advised though that usually there are waiting times of multiple weeks involved in obtaining this certificate. Please have a look at the immigration office's website for more details on how to obtain it as this process varies from city to city.
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