I am writing in third person, limited , past with half a dozen POV characters. I make an effort to never slip into omniscient and try to keep my character POVs in their own voices i.e wheel of time. My problem is that I tend—with one character especially—to give a lot of their personal thoughts, reactions etc. My question is how far can you go before it needs to be in the first person.
There are no rules, really. Or, to put it this way, there are conventions, but that's precisely where a skillful writer comes in. A skillful writer, in control of her art, is able to see when something works and when something doesn't. Narration perspectives and focalization are no exception.
The best advice I can give you is this: Don't focus too much on what you're supposed to do; focus on the best way to convey the message, then pick whatever method works for it, both locally (i.e. in a specific scene) and globally (in the entire book). What I mean by that? In an otherwise 3rd-person narration, if you really want to accentuate a feeling, you can switch to 1st-person (perhaps with italics), to indicate inner thought. But if you plan to do this extensively, it a) loses its "exclamation point" quality; b) you have to be consistent - in other words, if a characters stars having inner dialogue like that, you can't just stop it at some point without a reason
Intimately deep third-person limited POV is wholly acceptable and can be just as intimate as first person. It seems to work well to start scenes or chapters in a more shallow POV to establish the scene and then progressively get deeper. As a scene gets more intense, the POV should get deeper. When you want to back off the intensity, get shallower.
I admire writers who can do first person well, getting very detailed while still believably sounding like someone telling a story of what they experienced. But first person is more challenging than third person when working with a character with impaired self-awareness, such as a schizophrenic character I'm currently using. I found I needed a more objective description of her experience than was plausible to relate in first person.