If you want two moons, your only choice is to blow the moon up into bits and pieces. Then work on getting those pieces to coalesce into two moons.
A more worthwhile effort would be to build a huge observatory and base smack in the middle of the far side. You'd get about 6 weeks of unobscured viewing. You'd relay data back to earth via satellite in lunar polar orbit.
I think the Chinese will do this (the observatory and base).
Whenever Superman pushes a planet, somewhere to the people who observe it, he looks like he's just doing pushups.