Sounds more like Voltron than Thundercats, but I guess I just remember the personal storyline feel coming out of the Thundercats cartoon. It has been long enough I may be forgetting complete portions of it if it didn't resonate for me for whatever reason at that age.
However, there are actually rules for building a squadron where each player has their own starship. It also includes discussion about having a HQ ship. Archives of Nethys Reference https://aonsrd.com/Rules.aspx?ID=558
I thought I'd seen rules for dealing with ships merging together. But I can't seem to fine it right this second other than Hive Joining, which is specific to Xenowarden pods joining together to make a Xenowarden arkship. But I would think you might easily be able to imagine using the squadron rules to determine the Tier of the sub-component ships, and have them operate as ships of those tiers. Then if they merge, have them become a ship of the 'party' tier, representing the combined power. I'm not certain exactly how you would deal with the damage on the individual smaller ship when they merge together, and what to do with glitching systems, etc.
Guess what... I findally found it, it is refered to as Unification Matrix and is discussed in the rules I'm linking for you to look at. Isn't it funny that you can't see something you are actually looking directly at. I thought I thought it would show up as a subheading, not just a device/system.