Technically you could. There's no limit as to what you can put into the kit geometries, it still all gets weighted to the same 3p skeleton. The trick would be to superimpose a different player model (as part of the kit model) over the original player model so that the kit model covers the underlying player model at each time. Also the vertex weights would have to be matched to the original player model, otherwise parts of the original model might be visible during certain animations.
But covering everything is going to be pretty hard and most likely would result in strange-looking proportions for the new model.
Doesn't mean you wouldn't be able to replace or add smaller stuff like wedding bands, scarves, red cross armbands for medics, glasses, etc. in the kit geometries for a wider variety.