Yes, having other charge sources (including other manufacturer's charge controllers) in parallel with Morningstar TriStar may work. You will want to match all of the charge settings as close as possible. Below are some helpful links:

Morningstar Parallel Charging Using Multiple Controllers with Separate PV Arrays

Morningstar Connectivity Manual - Networking and Communications

Can I use different brand charge controllers in parallel with a TriStar charge controller and that will "talk" to a lithium battery management system (BMS)?

As of the date of this blog, Morningstar charge controllers do not "talk" with a lithium battery management system (BMS). As for a BMS being able to talk to various controllers in parallel, that would be a question for the BMS manufacturer.