My problem is how i should vent an additional bathroom that i would
like to add to my 1930 house. It currently has only 1 bathroom, which
is on the 2nd floor. There is a 4" drainpipe and a 3" vent, both of
which extend from the basement to the 2nd floor (and the vent thru the
roof). It's impractical for me to add a new bathroom either near the
existing DWV lines, so i would have to convert a mud room in the corner
of the first floor house into the proposed bathroom. I can easily add
a drain from the mud room into the basement, but i don't know where i
can add a vent pipe. Adding a bathroom would be impractical if i have
to tear the house up to add new vent pipes.

Here are the options that i can think of so far:
1)Is it acceptable to have a vent pipe that extends upward @6" from the
trap, then back down into the basement to connect to the vent pipe
there? Or do i have to have the vent pipe travel upwards and over to
connect to the vent pipe above the highest trap in the house?

2) can i get away with a "cheater valve" which means i wouldn't have to
install new vent pipes?

3) do i need a separate vent pipe at all? if the waste line is 4",
might there always be air in the line to serve as a vent?

I live in Massachusetts, and i'm having a hard time interpreting the
state plumbing code. I don't plan on doing the work myself, but i
need to know if this is even feasible, and i want to know if i should
be suspicious of a plumber who proposes the most expensive solution.