BESM was surprisingly capable of handling superheroes. I never used it on that power level personally (all I did was generic, Lodoss War-style fantasy) but fellow BESM-philes swear on it.
BESM characters are built (point buy) from "attributes" (= feats, special abilities) that are effects-based, eg "Massive Damage" buys a fighting style/skill/ability that dishes out more damage than a typical attack, and it's the player's job to define source - is it a magical ray or bolt, or a holy sword, or a secret kung fu kick? All "attributes" come in 6 levels, with the highest levels firmly in super territory.
The beauty of BESM was that it was possible to "nest" attributes in others. You could buy the attribute "Own A Big Mecha" for 4 points and received 20 points for building the mecha stats and capabilities from the same attribute list as your character. So you could give the mecha the ability "Massive Damage" instead. The term "mecha" was just a placeholder, it could be any kind of vehicle, from Kaneda's motor bike to Iron Man's armor to the Millennium Falcon.
Spells were built in the same fashion.
I turned my back on BESM because I found it too crunchy on the GM side. Monster stats were as complex as character stats (as they were built, you guessed it, using the same rules) and I didn't need to know that green slimes had the defect "Cannot Talk" that gave them 2 build points for more attributes - especially when monsters could be built from any number of points the GM deemed fit.
I never tried OVA but from a read-through it seems like a more freeform spiritual successor of BESM.