In an office space that is shared by many different (small) companies, is it
possible to use only one wireless router, yet give each company its own
subnet (so that windows network shared files, even publicly shared, don't
leak out of a company).

I don't see how this could be done using a typical home wireless router,
since there is only one DHCP server.

So the only solution is to have one wireless router per company (that wishes
to use wireless). This may lead to wireless overcrowding -- afterall there
are only 3 non overlapping channels.

What is the typical solution to this problem?