Can there be a continuous transform between spaces with different numbers of dimensions? Strictly, no. In the limit, yes.

There are two main models for dimensions. Straight lines and circles. Each is a limiting case of a spiral. A spiral with no pitch is a straight line while a spiral with increasing pitch has as its limit a complex plane.

The transform one could use would be multiplying by a complex number. If the number is real then you get a straight line. If imaginary you get a circle. Anything in between is also possible. There you go, a continuous transform between a circle and a straight line, simple as could be. If you want to completely get rid of a dimension, shrink that circle to a point. That complex number becomes zero. Reverse the process to grow a dimension from a point.

This system is centered around a point, not coordinate-free. But special relativity is point centered too. Chemists who do calulations have to keep separate dimensions for every particle. If they have 25 particles they are working in a 100 dimensional space. This is why quantum computers are important: only they are practical for calculations in such spaces.