If your term of stay is going to expire, and you continue the same activities,
you can apply for the extension of stay.
You can apply for the longer term than you have now. But if you do so, it's not permitted necesarily. Immigration has the discretion. At least you can try it, if you want.
It takes 4,000 yen as a charge of immigration.
If you make this application and the new resident card is not issued yet, you can stay 2 month after the expiration date.
But immigration announces it's better you apply it 10 days to 1 month prior to the expiration date.
You have to file appropriate document to file this application same as when you obtain new visa. We can give you appropriate consultation, go to immigration and file application instead of you.
Normally you have to go to immigration twice, upon filing application and receiving new resident card.
You may be treated unfavorably, like you can get only short term, if your behavior is not good enough. Please see the pdf below.
Guidelines for Permission for Change of Status of Residence and Extension of Period of Stay (Revised)