What's the purpose of a 2nd soil stack?

I was looking over the DWV pipes in my basement and realized I have 2 soil stacks (if I am using the term appropriately). As you can see, there is the main 3" one on the left, but there is this separate 2" one on the right. I tried to trace the lines, but can't really tell what the 2" line goes to. I have a 2-story house if that helps - the 2" line heads upstairs but I have no idea why I would need that separate line right there and can't think of any drains in the vicinity where it goes into the next story.

The other weird thing about the 2" line is the short stub-out you can see in the left pic - that is in the joist space.

Any ideas what this 2" line might be for, and why it has that stub-out?

Thanks.

That right hand pipe is the vent for the laundry trap, or in your case the softener discharge line and future toilet. The tee is probably a "future" provision for a basement bathroom. The REAL question is "What is the white pipe connected to the large black one". IT is the "improper" one because it has negated the "necessary" cleanout on your main line.

Thanks, HJ -

I figured someone would call me on that connection connection. The previous homeowner plumbed the sump pump discharge there instead of having it go out to the lawn as originally designed.

1. some areas do not allow a sump pump to discharge into the sewer because it overloads the treatment plants with water that does not need to be treated.
2. If it was going to be connected, it should have been done properly, NOT the easiest way.
3. If, and when, the sewer plugs up, that connection will have to be cut out to access the cleanout, and if the plumber is conscientious, he will reconnect it the proper way.

It looks to me, that the 2" pipe on the right is a vent for the downstairs toilet, and someone installed a washer drain in the vent instead of from the 3" stack on the left.
So that 2" line going up through the roof, perhaps had a stub for future venting of the washer which would have been plumbed on the other side of the 3" stack.
Of course like hj mentions, the cleanout should be re-established.

Thanks, gentlemen. Makes perfect sense.

One of the more interesting challenges is figuring out WHAT the pipes were intended for AFTER the concrete is poured.

I bet!

Sounds like detective work - looking at clues and making educated inferences.