What you're describing is classic back-to-back ticketing and is not allowed.

However, what you can do in this situation where your city is expensive, is stage yourself to another city that's both cheap to get to, and less restrictive to get in and out of.

The fare IAH-JAN + JAN-ORD combined is less than IAH-ORD without a Saturday stay.

So IAH-ORD-IAH = $575, but IAH-JAN-IAH-ORD-IAH-JAN-IAH = $374. You can do it all on one ticket to protect yourself, or you can split it up on two to get two online booking bonuses.

There may be other cities, so poke around some more...