One solution is an air admittance valve or aav.
Aav vent for toilet.
However before you begin installing an air admittance valve check with your local building inspections office as local codes govern the use of aavs in place of vents.
This negative pressure causes the vent to open and let in enough air to relieve the pressure.
When it opens air is allowed to enter the plumbing system.
A toilet will work just fine without a vent and in your situation it wouldn t affect any of the pre existing devices because they all have vents.
Then gravity closes the valve keeping sewer gases out of the room.
You may also be allowed to wet vent the toilet via the sink.
Most inspectors won t approve an aav unless it is the best solution of a bad situation.
If possible you might attach the new sink s vent to one of the others to the right in your diagram.
The device shall close by gravity and seal the vent terminal at zero differential pressure no flow conditions and under positive internal pressures.
An air admittance valve is a 1 way valve designed to allow air to enter the plumbing drainage system when negative pressures develop in the piping system.
My guess is that you d put one aav in the vanity for the sink and use aavs in unfinished space perhaps on the other side of a wall for the other fixtures.
Depending on the valve and the size of the vent aavs can support one or multiple vent lines.
Air admittance valves aav are one way vents installed after the trap on the drain line of a fixture.
Watch this video to help understand how a plumbing vent works.
They re designed to address negative air pressure in the drain system created when a fixture is drained.
Sweet spot sealing technology ensures optimal valve opening and closing.
This one way valve is designed to allow air into the plumbing when negative pressure is developed from draining.
If you re wondering how studor vents work after the toilet is flushed the water flows down the drain resulting in negative pressure.
Studor vents are a very popular kind of air admittance valve that works really well.
Abs air admittance valve allows air into a plumbing system without using a vent extended to open air and keeps sewer gases from escaping inside of a building.
That s money in the pocket for the plumber.
In the event that your walls do not leave enough space for any of the above vents then the local code may allow you to opt for an air admittance valve aav.
An aav can significantly reduce the amount of venting materials needed in a plumbing system.
The oatey sure vent 1 1 2 2 in.