Subsite on parked domain?

– I have two domains….domain1 and domain2
– I have domain1 set up as a multisite and is working great
– I have domain2 set up as a parked domain and is mapped to domain1
– These are to be completely independent sites to the end user.
– I am on a shared server

My question is this: I need to make domain2 act like a multisite. Is this possible? Can I make a subsite for domain2 if it is a parked domain mapped to domain1?

Thanks in advance for any help.