I have a German business visa, but soon I will have new type of visa (family visa). Is it possible to have both visas at the same time, or will the German embassy will cancel the business visa?
The Handbook for the processing of visa applications (an official document with a list of guidances for Schengen consulates) contains the following recommendation:
A holder of a multiple-entry visa may apply for a new visa before the expiry of the validity of the visa currently held. However, the validity of the new visa must complement the current visa, i.e. a person cannot hold two uniform visas valid for the same period in time.
Therefore the answer is that you cannot have two visas for the same time period - either the second visa will start after the first one or the first one will be cancelled. However note that consulates sometimes make mistakes with this rule, so it's technically possible for a person to have overlapping visas, if the consulate makes an error.