Imagine this diagram with the middle "Four way switch" missing so that
the top yellow terminal on the left switch connects to the top yellow
terminal on the right switch and the bottom yellow terminals on both
switches are connected together too.
That is the wiring you have when you have two separate "three way
switches" controlling the same light. And, as you can see, no ONE
switch determines whether the light is on or off. Both switch toggles
have to be in the up position, or both in the down position, for the
light to be on. So, fliping EITHER switch toggle turns the light off,
and flipping it again, or flipping the other switch toggle, turns it
back on again. So, with two "three way switches", both switches have
two different "ON" positions instead of an ON and an OFF position like a
normal toggle switch. And, whether or not the light is ON or OFF
depends on the position of BOTH switches.
Now, if you want a third switch to control that same light, you still
need both three way switches, but you also need something called a "4
way switch" shown in the middle of that diagram.
If we number the contacts starting with #1 in the top left corner of the
4 way switch and going clockwise, when the toggle of a 4 way switch is
in one position, it connects contacts 1 and 2 together and 3 and 4
together. If you flip the toggle to the other position, it connects
contacts 1 and 3 together and 2 and 4 together. That way, regardless of
what position the two three way switches are in, flipping that middle 4
way switch will turn the light on, or turn it off.
In fact, of you wanted MORE than three switches, all of which would turn
the light on or off, you'd simply keep adding 4 way switches between the
two three way switches. That way, no matter what position the two three
way switches were in, flipping any of the 4 way switches between them
would turn the light on or turn it off.
So, it seems to me that you SHOULD be able to do what you're wanting
1. Inspecting each switch that controls that light to determine which
are your two three way switches, and which are the 4 way switches.
2. Checking each of the intermediate 4 way switches to find out which
toggle position results in terminals 1 and 2 being connected and
terminals 3 and 4 being connected together. You want each intermediate
4 way switch to connect 1-2 and 3-4 when the toggle is in the down
3. Now, just turn EITHER one of the two three way switches on the end
upside down. That way, when it's toggle is in the down position, the
light will be off, and flipping the toggle of ANY other switch will turn
the light ON.
Now, the wiring can get pretty hairy because the power won't necessarily
come into the electrical box at one end of the room. The power could
come in at the light's electrical box, or at the electrical box of any
of the switches.
But, as long as you understand the principle involved here which is to
set up all your switches so that the power goes through all the top
terminals when the toggles of the two three way switches are up, and
through all the bottom terminals when the toggles of the two three way
switches are down (and you may have to turn some 4 way switches upside
down to ensure they're all oriented the same). In that situation, with
the toggles of both 3 way switches on the end in the down position, the
light will be ON. By turning either three way switch upside down,
having the toggle in the down position will interrupt voltage getting to
the lamp, so that with one three way switch upside down, ALL toggles in
the down position means the light is OFF, and flipping ANY switch turns
the light ON.
Hope this helps.
Maybe draw the terminals of 4 switches (two three way switches on the
end and two 4 way switches between them) and connect the terminals with
lines to show where the electricity will flow, and you should see how
the above plan will work. Or, at least, it seems to me, how it should
work to accomplish what you want.