Yes, you certainly can. You can request an extension every year or every four years, depending on the type of permission you have. A temporary permit must be renewed every year, whereas a continuous permit must be renewed every four years.
At least three months before your permission expires, you should request an extension.
You can apply for a residence permit after living with a continuous permission for around 5 years, which is valid permanently unless there is a reason to revoke your residence.