First off, very nice looking drawing.
There are a few things to change though.
I hired a plumber from Iowa that would have plumbed the basement like yours.
I couldn't let him do any waste and vent layout in the Seattle area.
We were using the UPC code, which I believe Iowa does too. I couldn't see any awareness on his part that he had ever used it.
Every trap should be vented, and you can't use the stack from the upstairs plumbing for your vent.
If your stack has plumbing waste from upstairs coming down it, it's not a vent.
When you lay the waste line on the horizontal and run other waste lines in, they're not vented either.
If you had a vertical vent stack, you could get a two way or three way fitting and run that many fixtures in, if they combine at the same level.
You can't just branch off and add fixtures as you go.
Fittings that are on their side must be wye fittings, not santees.
Below is a drawing that shows two bathrooms with venting that are stacked.
You will see from the drawing, that one vent through the roof will suffice, if everything is tied back together.