I am planning a new addition to rear of home and the existing aluminum siding is in good shape but not manufactured any longer. Can I install a vinyl siding to the new addition and can it be joined at the corners with the aluminum?

Got a picture or a at least a drawing?
Alumium siding is a real pain to try and tie into.
When you try to take it down you start at the top, the first piece will always be damaged.
Aluminum uses a differant width J, inside and outside corners. If you try and and slip vinyl into a aluminum trim piece it will be to tight and tend to hold the siding in place with can cause buckling and seams to open up.
Without a picture of where you plan to build this addition it's hard to suggest how to make all this tie in.
Anything can be done, some just take a little more head scratching. That's why I'm bald on the back of my head from scratching it and saying "what the heck am I going to do now".
What's the exposure and finish on the aluminum siding there now.