I've not done it enough times to know for sure (I'm not a regular, the closest tank center is about 3 hours away), but on subsequent visits it is much easier to get the first "rock" off. I imagine yes there would be more based on my experiences. You start to get more in tune with your body and I'm pretty sure I didn't uncover everything. I know for a fact there's something still in my neck that I can't get rid of even in the tank, but they even tell you that the neck is the hardest part for new people to figure out what to deal with in those things and give you tips.
It's been years since I've gone, and I feel like I need to do it again now. I've been considering purchasing one for myself (they are starting to get cheaper and more efficient for in-home use).
Also for tips on what to look for, there are people trying ideas with listening to music, playing TV documentaries to help you learn, etc while doing it. That is definitely not what you want. Even the slightest light is not something that is worthwhile, you want complete darkness. No music either. I think most of those places offer you the option of either if they offer those things, but go for the complete sensory deprivation experience. Your imagination fills in the blanks on its own.
I just relooked and there is a closer float center ~2 hours away that just opened up. Just booked a float this weekend. Thanks Hubski for forcing me to be chill. You're such a drag. :P