I believe this is a bit more complicated than simply enlarging the width of the datapath; that is, the operands and output of the ALU to 32-bits. There is a question of what to do about data memory. It could be altered to implement 32-bit addressable words and make the data bus 32-bits wide. This approach seems reasonably straight-forward since in the Hack computer, the instruction bus is completely separate from the data bus (Harvard architecture) and could remain 16-bit if desired.
There is a difficulty with this approach since the data Memory "chip" created in the final build of the Hack computer utilizes several "built-in" 16-bit chips. so you would probably have to go to the underlying Java code to make the change to 32-bit. There would probably also need to be changes made to the screen and keyboard I/O internal routines to accommodate the change to 32-bit words and the accompanying bus.
Another approach commonly used in many commercial byte-addressable microprocessors would be to leave the memory alone and handle 32-bit ALU operations in 16-bit chunks. I think this would be more complicated, but I have not really thought much about it. This would seem to move the Hack CPU into the CISC realm and would not be in keeping with its KISS design philosophy.