Thank you for sharing your question with the Wefugee Community!
In general, it is only possible to extend a visitors visa, if it is not expired yet.
If the visa is still valid and there are very strong reasons (i.e. sickness or humanitarian issues), the local immigration office (Ausländerbehörde) might issue an extension in exceptional cases.
A family unification visa would require a marriage or at least a planned marriage. Please check this thread, which provides some useful information on this.
Without knowing your background of education and/ or professional experience, you also may think about your possibilities of applying for a work visa for Germany. However, you will probably need to apply for the latter from your country of origin.
Please feel free to get back to us with any further questions and all the best,