@Dadadada
Hey
Hve you checked to make sure your DHCP has enough leases for that many clients? 32 seems a strange but logical amount (deterministic binary number). What actually happens when you hit the 32? Any specific error pops up? Also are these on the 2.4 or 5Ghz?
I cant comment on the exact amount this will support, however if honest connecting 60 devices to one AP is a huge ask. I install TP Link Omada EAPs for a living and when we start passing 40 devices we recommend an 2nd AP, given the Omada line is a business grade device which can support 60 connections fairly easily, the VR range is home grade and 60 is a big ask. Being totally honest with you, I would recommend you start to split your network. The VR600 v3 supports OneMesh so that might be a consideration for you by adding sub nodes to take the load down.
I do have the VR600 v2 myself and I can push 30 devices, but performance will suffer with that many clients.
Hopefully one of the TP Link admins will have that answer for you