We have a Laundry in our basement. It works fine. The drain goes through a trap and into the slab (three feet into the room.) We don't know where it goes for sure. We think it's Grey water because the sewer pipe is over four feet up off the slab and exits through the front wall toward the street. No sign of a French drain either.

We're concerned that the Grey water drain is contributing to the settling of the non-basemented 1/3 of the house. (built without a footing no less.)

System consists of; Single 4" vent stack with 1-1/2" tub-1-1/2" sink-4" toilet (all close), turns level (has OK slope) and runs 16 feet at about 5-4 feet high then through the front wall, 2" vented kitchen drain runs 25' before joining this mess that hangs a foot into the room.

We want to replace the 4" Iron sewer pipe with ABS and tuck it up higher and closer to the wall in preparation to finish the area.

It might be nice to drain the laundry into the (raised to 6'+) sewer pipe.

Can the clothes washer pump that high?

I have seen it several times in my customer house who had similar situation as you. Washer has pump that will pump up water 6' hight. But it creates one problem: Once the pump stops pumping there is 6' worth of water inside that vertical discharge pipe. That water drops back to your washing machine. It is a lot of water. You could install back-flow preventing valve to prevent this from happening. But I am sure, any kind of valve on discharge pipe is against manufacturers recommendations.