It depends on which vines you have. It could cause a problem if they intertwine and then need different care or pruning. And they would all need to be of equal vigour so one didn't drown out another. Imagine trying to untangle the dead vines of one which dies to the ground each winter from another which might be evergreen and permanent. Some vines will behave well together, others will fight. More specifics needed to know which situation you might have.

When I've mixed vines before, they didn't look that good. The overall effect was messy and weedy-looking.

I think that different colors of the same type vine might look nice mixed together, though.

I've tried mixing vines on a trellis several times and this is the only combination I've ever been happy with. Usually one will completely overwhelm the other, or one will be dormant and look ratty while the other is trying to bloom. These vines are a red crossvine and a yellow honeysuckle. The cross vine blooms in the spring with a few blooms in the fall. The honeysuckle will usually start blooming while the crossvine is in full bloom, then continue to bloom all summer. They are both evergreen, so I don't have to deal with one going dormant while the other is still blooming.
Jim