Is it possible?
Yes, and there are many instances. A system is often described as moving in a "state space". That ascribes dimensions to all sorts of characteristics, such as speed, potential energy, temperature... whatever you like.
The number of dimensions used to describe spaces is the minimum number of independent co-ordinates needed to specify a point in that space. The co-ordinates may be any units you choose.
Could reaction (aka acceleration) be considered to be a dimension. Things don't just move through time and space; they also react to each other?
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