Moving W/D and floor drain
I have a 10 year old home but an expanding family has us cramped for space. We need to reno the basement to get a little more living space but to save a buck, the developer/builder decided to separate the utilities into all three basement rooms leaving me with very little useable space. I'm looking to relocate the washer and dryer and move the existing floor drain from the 'current utility room' to the 'proposed utility room' (in green) in the annotated floor plan attached. I've drawn in the location of the various 3" stacks as well as their path to the final floor clean-out at the front of the house. Note that neither of the optional cold-storage nor the 3-piece rough-in apply. Also, the HW tank and furnace are not where the plans specify, but that is left for another thread...
While I'm pretty confident about cutting the concrete in the 'proposed utility room' and installing a laundry and floor drain, my concern is venting. The three stacks shown correspond to the three bathrooms on the main/upper floors. They are obviously a fair distance from the 'proposed utility room.' The existing laundry tub and washer share a 1 1/2" p-type trap and is then vented 1 1/2" before entering the stack in the corner of the 'current utility room.' This 1 1/2" vent is also used for the kitchen and there are no other vents that I can see. That is to say, the closest 3" stack (which serves a 2-piece bathroom on the main floor) doesn't tie into any vent that I can see. So, what are my options here? Can run a pitched 1 1/2" vent from the 'proposed utility room' all the way into this corner? I plan on following one of Terry's suggested laundry rough-ins.
(A larger copy of the above can be viewed here)