The 289 has a 50 Ohm (full scale) mode which can resolve down to 1 mOhm, but the real problem with such low resistances is that the probe-to-test point resistance becomes very significant. It also varies a lot with contact pressure and cleanliness, so you can't just expect to zero it out.
Your best bet might be to pass a known current through the path you want to measure, then use the meter you already have in voltage mode to explore the voltage drop at various points - ie. do a 4 wire measurement, as already suggested.