suppose you are measuring a point on in a room. it can be x from one wall, y from another, and z from the floor. but what if one were to measure an event that took place at a point in this room? to do so you must introduce t.
Since you are talking "coordinate systems" which are mathematical constructs, of course there are. If, for example, one were working on a problem involving all spheres, which can be identified by their center and radius, it would make sense to use a 4-dimensional space: 3 coordinates for the center and the fourth for radius.
It's not uncommon for physicists working in statistical mechanics to use an "n-dimensional" space where n is some huge number: 3 times the number of particles involved.
And, of course, "functional analysis"- used in theory of differential equations- regularly works with infinite dimensional spaces.