since plenty of 32-bit operating systems support more than 4GB of RAM. I believe even the server version of Windows does.
No, no and no.
32-bit is 32-bit whichever OS.
What you can do on 32-bit Windows Server and 32-bit Linux is use a hack called PAE. But its a nasty hack, and runs the risk of incompatibilities and bugs rearing their ugly heads. Even with PAE, the maximum memory a single process can use is 4GB. PAE is
not equivalent to a 64-bit system - infact, to be pedantic, turning on PAE just bumps 32-bit up to 36-bit !
The only answer to more than 4GB is to use a 64bit OS.