How to connecting addition frame to existing rim joist
You'll need to use hangers regardless. Face-nailing (as I assume you're implying by your mention of a "standard frame") isn't adequate to carry joists. They need actual bearing. 

An alternative could be a new ledger set below the existing rim joist, itself mounted with structural steel ledger hangers, on which the joists rest. I suspect that your inspector would still require a more substantial wall connection for each joist, though.