Is it possible to cross from a national park in Kenya e.g. Maasai Mara, into a national park in Tanzania e.g. Serengeti?
Yes and no.
Yes, you can cross over from a park in Kenya into another in Tanzania by first backtracking to a customs post outside the park, getting clearance, paying the necessary fees, and then going on into Tanzania.
No, you cannot just cross over from a park in Kenya to another in Tanzania without first clearing with immigration.