I do something like that.
I use shaving soap for the first two passes.
I use soapy water for the last pass.
I use shaving soap for the first two passes.
I use soapy water for the last pass.
This is why God allowed mankind to produce fantastic adjustable razors! So much easier than changing out to a different razor for each pass.I agree with @Eben Stone that you must be using inferior soaps.
There are some superb soaps that will do it all. They act as a preshave. For the shave, they provide superb slickness. They provide superb cushion to protect your skin from the blade. Finally, they provide superb post shave skin moisturizing and conditioning.
On a slightly different take on a similar topic, I DO use different razor and blade for every pass as I have found that each pass as a different requirement for efficiency and aggressiveness. Thus, I start with a very efficient razor to knock down my beard growth and complete my shave with a very mild razor equipped with a super sharp blade to pick up any stray stubble left behind by previous passes. I can use a single razor and blade for the entire shave, but I get better shaves using multiple razors.
I do have one adjustable razor, the Parker Variant. However, there are lots of variations in razor types. I have straight razors, three piece DE razors with open combs, three piece razors with safety bars, razors with slant heads, TTO razors, single edge Schick style injector razors, SE razors that use AC blades. I enjoy using different razors and using a differernt razor for every pass allows me to get a more enjoyable shave. However, I can use a single razor for the entire shave, I just do not enjoy doing it that way.This is why God allowed mankind to produce fantastic adjustable razors! So much easier than changing out to a different razor for each pass.