Not something I'd recommend :-) Montanas are pruning group 1 (no prune) and tanguticas are group 3 (hard prune). The two vines will become so intertwined it would be nearly impossible to isolate the tangutica for pruning. And to leave it unpruned indefinitely will result in a very unpleasant looking mess. Also, if you were to just prune the two together simultaneously, you are going to mess up the bloom season for at least one of them, depending on when you prune.

Do you think I would be able to prune the tangutica in the fall after bloom? I never prune the montana, unless we have a really bitter cold year. does any one have something planted with a montana that works? Thanks

How will you separate the tangutica from the montana in order to prune? The vines will become so intertwined I can't see how you can disentangle one without damaging the other.

I don't ever recommend planting two such robust vines together, whether it be clematis or any other vigorously growing vines. Second, unless you are prepared to deal with a very messy appearance or sacrifice a bloom season, I don't recommend combining two different pruning groups together.

But it's your choice - you can do what you like :-)