Not with a cookie and Defiantly not through using Muse.
You need an API solution to link your site and the 3rd party data together securely.
For clarity, are you saying that I would have to move away from muse?
Well you cant code the solutions needed in Muse to do this. You need a server running server side code to sync the CRM with BC to 3rd party just to begin with. Muse can not make semi complex sites let alone API work