I do this all the time. I use 8x10 paper to make a good print. Split contrast printing sequence etc.

Then, I often make an 11x14 or sometimes a 16x20. I have a Jobo Colorline 5000 analyzer. I use the Integrated mode with a diffuser over the light meter cell and I hand hold the diffuser over the enlarger lens and take an integrated density reading over the center of the print. I write down the density on my greaseboard. Then I raise the enlarger, compose the print with the same proportions as the 8x10, place the meter in the center of the print, and then open the aperture of the lens until I have the same density reading on the analyzer. That way, I use the same exposure times and sequences programmed into the RH Designs Stop clock timer. (the Darkroom Automation timer and meter would work similarly I think and be less expensive.)

It is remarkably accurate but not perfect. Sometimes the larger print degrades a little and needs a bit more contrast e.g. 1/6 stop more magenta exposure when going to 16x20 but I think the process saves me some time and paper.