Apollo 17 was the longest duration mission of the program, at 12 1/2 days. Let's assume that by flying a single crewperson, and taking aggressive power-conservation measures and extra snacks, we can extend the crew and spacecraft's endurance to 50 days. 

An elliptical orbit around Earth, with an apogee of about 1,140,000 km and perigee of about 200 km, has a period of about 50 days. That orbit is comfortably within Earth's Hill Sphere, so from LEO, only a single apogee-raising burn needs to be done; if we save mass by not fueling the LM, the S-IVB should be able to provide the needed ~3170 m/s of delta-v easily -- it's only 140 m/s more than a normal TLI!. We'll keep the rest of the LM to give our crewperson a little more living space. Almost all the maneuvering capability of the CSM goes unused; we'd want to make a short burn on the return leg to slow our return velocity to match the usual atmospheric entry velocity for a lunar mission (but we're really not coming back much faster than usual, and I believe there was lots of margin on the heat shield). 

That orbit takes the spacecraft to just about three times the distance from the Earth to the moon. As any experienced player of Kerbal Space Program knows, the rate at which apogee increases with increasing delta-v applied at perigee is very nonlinear -- it's much, much harder to get the apogee from 200 km to the moon's 384,400 km (~3030 m/s) than it is to raise the apogee from 384,400 km to 1,140,000 km (~140 m/s).

By burning some of the CSM's surplus ∆v on the injection to speed up, and the rest to brake at the 25-day mark, this could be increased a *lot*. Assuming we don't take the LM in this case, for simplicity, the CSM has about 2800 m/s of ∆v capability; reserving some for midcourse corrections, expending 1325 m/s times 25 days works out to another 2,862,000 km traveled, for just about 4,000,000 km apogee -- more than ten times the distance to the moon (and not even a tenth of the way to Mars). 

If we retain the LM's fuel and burn that on the outbound leg, then discard the LM for the "boostback" burn at 25 days, we can probably increase the range still further, but I'm not up to doing the math.