There will be issues whichever way - so you need to pick the right way for you at get it right first time.   In short - and from experience  on both sides - I'd say transfer now to your server, as separate branches. This may involve some logistics for connectivity (I don't know your set-up) but on the face of it - is better than running multiple servers and multiple business processes. You'll thank yourself in the long run   Moving / migrating / transferring / consolidating to one branch - on the same server - is far, far easier to manage once the data is on one platform. Trust me on this.

We were thinking to merge on our system but can well foresee a few issues 🙂  

not to any great extent so this shouldn't be a problem but thanks again  

Sorry Sandra - Are you planning to merge the branches on THEIR system - or merge and migrate to your server?   The first is as everyone has said above - the latter is potentially a whole new world of complexity - x 10!

Just thought, do you/they use Open Attach?