You can consider as many dimensions as you want. As I mentioned, for some time we had three papers regularly delivered, for additional perspective.

However typically, a single dimension is a useful first-order approximation[1], and so that's what's done in politics as well. As with all approximations, sometimes it works well and other times it does not.

[1]: https://en.wikipedia.org/wiki/Order_of_approximation

That was probably mentioned from US-centric point of view where they have two-party system.

I'm from Norway where we have currently ten parties in our parliament[1].

We still mostly talk about them as distributed along a left to right axis. Though as I mentioned it's not a perfect approximation.

[1]: https://en.wikipedia.org/wiki/Storting

Seems like Norway has also many constituencies which can favor dominant parties. However unlike US you have also leveling seats which balances it a bit.