There was a game out for a while called CthulhuTech. It combined anime giant robots with Lovecraftian forces. I flipped through it at the game store and skimmed over the background, but at the time my gaming friends had moved away and so I didn't buy it.
The basic idea is that human scientists have been working to understand the sort of sanity-rending "secrets man was not meant to know" type of science. And with large corporations and legions of researchers, they manage to do it. Each scientist works for maybe a few months on a tiny piece of the puzzle, until they start to show signs of insanity. Then they go into years of therapy until they're ready to take another crack at it. When you've got an Apple or a Google putting their weight behind this type of research, you make real progress. No one person can comprehend the technology that comes out of this without going immediately mad, but with tens of thousands of people working on it in little bits and pieces, you start to get the type of futuristic technology you'd see in anime. Think the opening to Macross with the discovery of the crashed Zentraedi ship, except with the Necronomicon instead.
At the low end, you've got laser pistols, household appliances that never run out of power, rocket packs, etc. Everything is fueled by extradimensional energies. At the mid-tier, you've got Battlemechs and powered armor. At the high end, you have Evangelions.
Anyway, various Lovecraftian races who are in the solar system suddenly realize that humanity has cracked the code, and they weren't supposed to. No servant/prey race has ever figured out the science before. So Earth gets invaded by hostile aliens who also use giant robot suits, or sometimes are just huge Shoggoths or other terrible monster forms.
It's a Lovecraft meets Godzilla meets Shadowrun meets Robotech meets Evangelion type thing. Very cool as a setting but I'm not sure what sort of adventures you'd play in it. But it seems perfect for a very AU type of Battletech setting.