Is there a way to add external RAM (let's say 100 MB or 200 MB) in this audio buffer mixing context?
There are SRAM ICs / boards, however, don't expect 100 MB, more like 1 MB (with the pin numbers and connectivity / protocols that an Arduino offers).

With Flash you can get much further, but it can only be written a number of times; not sure if that suits your requirements.

Beyond that, I'm afraid the real problem is in the processing speed. Mixing 100 samples with 48 KHz stero would mean (48000 * 2) = 96 KSamples/s. Since the Arduino is only 16 MHz you have just 16e6/96e3 = 166 clock cycles to mix all those 100 samples. Probably way too less.

Update

Winbond is a brand that is supported by Arduino libraries and the biggest supported IC is e.g. W25Q128FVSSIG, which is 128 Mbit, thus 8 MB. For 200 MB you need 25 of them which is quite a lot, and not sure if there will be issues using so many (let alone the cost). For this you do not need a file system, however you need to write it per page (if you want to do it efficiently). Which should be ok, since the SD card also is read per page (maybe not the same page size though).
However, you still have to copy the Flash memory into SRAM to be able to process it, so it's not the same as SRAM. Getting 200 MB SRAM will be very costly.