Would you put 13" slicks on 10" rims?

On paper.
In reality , the narrower rim draws the bead in and bulges out the rest of the side wall.
This creates a rounder , wider sidewall......drawing the edges of the tread upward.
The " section width " will be greater with a narrower rim , but it doesn't allow for a full foot print.
Sounds like I need to figure out how to fit 12" wide wheels onto the car, bulging sidewalls and losing some footprint are not what I'm looking for.