Mips Storage Byte by Byte

Ok so let's say I have a value 0x00003534 where 0x34 is at the address 0x7fffffffa. I want to start storing putting the values in a temp register one at a time. So on the first iteration $t0 will look like 0x00000034. Then I move to address 0x7ffffffb and store in $t0 so it looks like 0x00003534. I'm able to move from 0x7fffffffa to 0x7ffffffb properly and grab the new value to be store, but when i try to put it in $t0 it just overwrites 34. I can't just LH and move it all at once because the value won't necessarily always be a half word. So I need to iterate through and store byte by byte until null is hit. Any ideas?