Designing power supply on two sides of the PCB
Designing a board to have components on both sides is very possible. It poses a bit of a challenge on assembly, so it will be more expensive if you let a factory assemble it, or it will be more work if you assemble it yourself.
Couple of things to watch out for:

power supply chips tend to produce heat. Now you have twice the heat in the same PCB volume, with less area to get rid of it. If this was close to being critical in the one-sided design, you really have to re-do your thermal design.
In a lot of places, you really want to make sure the ground below your SMPS works well – so, you'd have to place your components in a way that doesn't break the ground plane in places it matters. This is usually the point where you realize you need to do something else than moving things to the bottom of a 2-layer board and indeed need 4 layers. Which comes at a pretty steep price increase, so maybe look into highly integrated SMPS modules from Texas Instruments or from Murata, which might help you achieve high density without having to switch to 4 layers.
Not all SMPS components can be operated synchronously, should you wish to just increase the current capacity of the same rail. Your IC indeed can be driven from an external clock, which would facilitate that, but it's still a design effort.

If indeed just increasing the current capacity, it might be wiser to look into a larger inductance and if necessary a switch and controller that deal with higher currents.


If you instead need to generate another, independent, rail, look into multi-output switch-mode regulator controllers. It will probably use less space to use one of these on the top side of your board than having another supply at the bottom, considering that complicates design.