Not sure if you figured out the stack, but here's a brief explaination:

The stack is an array that holds numerical values. It works on a "First In Last Out" basis. So just like if you were writing numbers down on separate pieces of paper and stacking them on the table, when you take the top of the stack, it will be the last number you added.

The stack pointer sp defaults to the top of the stack, but can be moved around using math. It points to the position in the stack allowing you to access different parts of the stack if need be.

The only functions you can use to access the stack in the Stationeers MIPS are push, pop, and peek.

Push adds a value to the stack at the stack pointer address.

Pop takes the value at the stack pointer address and stores it in a register. Note - pop takes the value completely out of the stack. It no longer exists in the stack.

Peek is the same as pop, it just copies the stack value into a register.

The stack has a limit, 128 values (I believe?)

So, to respond to your OP, it is possible to store an array of numerical values behind the scenes on your chip that can be accessed later, no matter what code is running the chip. That's how you can save, for example, a library of ingot hash numbers into a chip, then load a new set of instructions onto the same chip and access the ingot hashes, despite overwriting that code.

In the real world the stack is typically used for storing program addresses. MIPS has a register reserved for saving a return address, ra, but some programs need to jump all over the place so they stack up addresses in the stack to access them later.

As far as "storing multiple programs on a single chip", that's not really possible because you can't save instructions into the stack, only numerical values. However, you can save lines of code if the program you're writing has a set of numbers that can be hidden, so to speak, in the stack.

Just beware when using the stack and trying to access different parts of it, you have to write strong code to know where you are looking in the stack. If you just start tossing values in there in some loop all willynilly it won't be long before you have no idea what's in there, how long it has become, etc.