I'm not entirely sure about what the exact MSU-1 specs are, so, someone correct me if I'm wrong, but, I think it is an extension to the SNES, such as any other special chip could have been, that just adds 4GB of storage (32-bit address space) that devs can use however they want. Storing audio and video are two "simple" ways to use it, but it could be used to add regular graphics and data too (?).
IF this correct, then I have two answers for you.
First of all, even though no cartridges were ever officially produced bigger than 64MB (512mbit), the address range available for ROM use on the console's specs is bigger than that. I looked into this a long time ago and I don't remember just how much you could have, but it's more.
If that isn't sufficient, keeping it to official hardware, there's the 64DD, but that's kinda messy and impractical to use for homebrew, I would say, plus very few people have one.
As for unofficial hardware, I don't know about the everdrive, but the 64drive allows direct access to the slotted SD card from software, so you can basically have multigigabytes of storage that way. Plus, the newer HW2 model has 256MB (that is, 2048Mbit, 4x the biggest released cart) of RAM mapped to the cartridge ROM address range, with RW access. I think you can even DMA from SD to ROM-RAM. You could use it as a large cache, as a slower RAM, or whatever really.
If emulator devs wanted that kind of functionality, they could copy that.