Although it's pushing it a bit, quite a lot of the (lvl80) 6-man content is duoble! (see what I did there) 3 would just open the floodgates as most of the 6 man content would be doable with 3. Some might require a lot of gear that you need 6 or 24 to get, but if your goal is to duo stuff at some point that's certainly not a problem and will most certainly provide you the challenge you're looking for. You might even find that 3rd person along your way. And there's a pretty easy controllable gear threshold in wether you trigger HM or not as some NM khitai dungeons are even soloable with gear/patience.
Check out sardanapal's goofy tactics videos on youtube, solo vortex NM (no.8) and duo vortex HM (no.14) for example.
As for lower level dungeons, almost all of them are again soloable once you gain enough levels, but then again the challenge/reward will also diminish. But say, at lvl60 you could duo lvl40 dungeons and still get gear that would be an improvement? Maybe?