Planning new sink on existing drain

I'm planning on adding a small bar sink on the lower level of a split level home.
I need to know if I can safely tie it into the existing drain from the 1/2 level above.
I also need to know if there is any reason to tie in above vs. below the nearby cleanout on the existing drain.

The kitchen sink drain runs under the kitchen floor and down the 1/2 wall where the bar sink will be, then the drain enters the concrete slab and disappears to the sewer. I can't go into the slab for this project but I need to make sure I won't be causing any flooding by using the kitchen sink above the level of the bar sink.

Attached is a diagram.

Where is he vent for the kitchen sink? You will also need a vent on the bar sink after the trap and before the waste line your connecting to.

Thanks for your reply, John.

The vent in the kitchen is just behind the sink along the exterior wall so it's very far from the bar area. Also, the wall behind the bar sink is an open view between the upper and lower level, so there's no place to run a vent straight up behind the bar sink. Could I use one of those one way valve vents if I have it run a bit higher than the bar?

You can use what we call an AAV or Studer vent. It doesn't have to be above the fixture. But in your case it must be between the trap and the waste line the trap is connected to. It must also be accessible.

Boba, Is that a kitchen drain or a main line clean-out. Just curious

Thanks John, for all your help. I will be using the vent method you suggested.

IFIXIT - It's the drain from the kitchen, but there is a small clean out point on it just before it gets to where I would connect the new bar drain.

Personally I prefer my c.o. Above the tie in of the trap so if it backs up, you gotta a lot less mess to deal with water coming of to the c.o
Compared to having the c.o below the trap arm.