Can a multiplier be used to multiply larger numbers?
Yes, you can use a small multiplier to do large multiplication operations. As jippie says, it's exactly what you do when you multiply multi-digit decimal numbers by hand: You multiply each pair of digits in your head, and write down the partial results and then add them up. This is radix-10 multiplication.

You can do the same thing with 4-bit binary numbers (radix-16 or hexadecimal), or even 8-bit binary numbers (radix-256) or larger. The principle is exactly the same.

It's easiest if both numbers are unsigned. If either one is negative, negate it, and then later figure out what the sign of the result needs to be.