Nodal analysis - how to handle two adjacent supernodes
Don't get thrown off by having multiple voltage sources attached to the same node: just follow the super-node procedure, and recognize that it's ok to combine a super-node with another node/super-node to make a "super-super-node" (or just a bigger super-node).

In your case, you will eventually have a super-node which contains nodes 1, 2, and 3, and 2 other equations which describe the relationship between (v1,v2) and (v1,v3).

This gives you 3 equations and 3 unknowns, which can be solved using some algebra.

Finding these equations is left as an exercise for the reader (feel free to ask questions if you get stuck somewhere)