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Yes, if you use an REU, which is a correctly contemporary memory upgrade for the C64.

Expanding from Johnwbyrd's nearby:

-- Commodore sold a Ram Expansion Unit named "1764" to bring the C64 to 256kb of RAM;

-- it was possible to use the REU for the C128 named "1750" to bring the C64 to 512kb of RAM;

-- and it is possible to expand on that to have a 2MB REU for the C64 - see https://www.neperos.com/article/rlut8ce90fbb7701

You can have two megabytes on the C64, pretty "legally".

I can imagine "someone" back in the day could take PC SIMM modules and cobble together some monstrosity that would allow one to fill 16MB of RAM on a c64 using simple bank switching. However, the main "innovation" of these original and later REUs wasn't the memory amount, but the chip that implemented DMA. That DMA chip could be used to copy ram contents very quickly with minimal CPU involvement. This is why c64 equipped with the REU has much better graphics capabilities (used for background animation etc).

As far as I know, we still don't have an open source equivalent of that dma chip.

No, it's a Commodore 16384.

(The max addressable memory with a C64 REU is 16 Megabytes.)