Everything can be handled in a way to match.

One can hardly judge before seeing a visualisation.

I Personally wouldn't mix them all, but as Andreas said, it is possible i guess.

What are your thoughts about a sans like Gotham and a geometric like DIN together? Any examples of that working?

Worth magazine uses a palette that isn't unlike what you're describing. The substitute Didot for a more feminine slab typeface (not sure which one)... but it works really nicely for them.