Yes, you can use TAP links from as many agencies as you want.
TikTok's link limit is per product, not per agency
Each product carries one active TAP link in your showcase at a time. Add a new link to a product that already has one, and TikTok uses the newest link for all future videos and Lives; the old link is replaced automatically. So mixing agencies is fine, and the thing to keep track of is which link is newest on each product, because that's the one earning on new videos and Lives. A new link doesn't change videos you already posted.
Next steps
The questions that usually come with this one: