Can a processor with 16 bit address bus and 16 bit data bus access more than 16 bits of disk space?

Say for example, I have a drive the stores up to 4 GB of storage space, could a 16-bit processor be designed with 16-bit address space and 16-bit data space, but send multiple 16-bit words for accessing say, 32-bits of storage space? Like it sends the first 16-bits for the first part of the address and the next 16-bits for the rest of the address?