Multidimensional graphing

I’m not sure whether this is more appropriate as a graphing question or a stats question, but I’ll start here.

I would like to graph the positions of individual cases on several (more than 3) dimensions in two (or possibly three) dimensional space, similar to a biplot or correspondence map. However, I would like to be able to partition that resulting two or three dimensional graph into sections that I could use to define that multidimensional space when potting new data.

The goal here is to end up with a two (or three) dimensional space that is defined by several dimensions and can be used for plotting new data into that space without changing the spatial layout of the dimensions.

Any suggestions on how to do this in R would be appreciated.