If we define a core of a processor as the most basic unit the processor must have to still operate, then RAM does have something like that. Most RAM modules are made up of multiple memory chips and the number isn't always the same. Some can have 4, some can have 8, and some can have 16. Those share the load with storing data. If we expand this out further, the memory system in modern computers typically have multiple memory channels. You can still operate in a single channel, but for higher performance, multiple channels should be used.
Now if we're talking about RAM modules or pools of memory doing independent things, that too can be achieved. It's just not done so in practice because it doesn't add any real benefit.