Basement Bathroom Venting

I am in the process of finishing a basement bathroom. There is a 2 " vent stack above the rough ins for the sink, toilet and tub drains. My plan is to tie those drains into the 2 inch stack. My problem is my pit for my sewage ejector is about 20 feet away in another part of the basement. Can I continue this vent piping over to the pit and vent my pump as well?

I would have a tub, toilet, sink and pump all on the same 2 inch line. To my knowledge there is nothing else on this vent line and it vents directly to the outside.

Thanks

vent

Should be no problem as long as the pipe is sloped to provide drainage and you use a 2" pipe.