Interview Follow-Up: Timing

I had a first round virtual interview with a MM PE fund last Monday. It was with a principal, mostly just focusing on my experience and then with a small case study towards the end. I think it went really well, both from a fit perspective and from how I was able to articulate my investing experience. Case study also went fine.

Towards the end, I even offered to come in and meet some of the team in person, as I felt that would add a lot of value to the process, to which he agreed would be a good idea. He asked me if I had any time constraints on the interview process , to which I said no, because I didn't at the time. He then admitted that they were moving slow with bringing new people on board because they had so much going 

I haven't heard back from the principal, and I've since started a process with another fund which is moving a lot faster (I already have my 2nd round scheduled for this week). However, I'm more interested in this original fund for a variety of reasons. 

What's an appropriate time to follow up with the principal and re-iterate my interest? Should I ask if he has any news on next steps or see if there's a good time for me to come in and meet the team in person?