You can do most of the 2-man heroics, a few of them may require assistance especially as DPS. Just remember to be picky and not to give up after some wipes.
In particular on Coruscant I saw people asking for Republic's Most Wanted, solo'd both on my Sentinel (hardest) and Commando (easiest). It's really a tougher 1-man heroic yet I saw people going in with 4 :/
If you're tank or healer even 4-mans can be solo'd (to a (very) large extent), so can the champions (so happy I killed my arch-nemesis Yanu Selke on Quesh). Some are quite fun to solo, like Building a Better Beast on Nar Shaddaa, cleaning up the entire room felt satisfying, lots of XP, lots of decent loot and cash ofc.