In a sink located in the second floor apt kitchen the drain line under the sink draining away from the sink pitches upward into the soil pipe causing the sink to back up. What should do to remedy this? Should I also remove the old soil stack going up to the roof because of possible blockage in the stack and condition of said stack.

If the bottom of the sink is below the soil pipe, likely you can't fix it with raising the sink. A shallower sink might work. I actually had to raise a sink slightly that had been lowered to give children access. The children could still reach it with the bottom of the sink just above where the drain pipe went into the wall. It was more of a carpentry job than plumbing. The faucets were on flex, and I just added a new longer tail stock.

As long as the sink is above the drain, the sink should drain, although water would stand in the drain up to the level of the drain. Did it ever drain? If it did in the past and doesn't now, it may be clogged. If plunging or drain cleaner doesn't work, you need a snake, yours or the plumber's.

They put vents in because drains don't work right without them. Think replace, not remove if it is in bad shape.

Good morning Gerard, I don't know how bad your soil stack is but you're sugesting major surgery for a minor problem. If the pipe going into the wall has backpitch take the trap apart at the nut and shorten the tailpiece that connects the drain to the trap and reconnect. If there is a kitchen directly below the second floor apartment and the sink drains OK then the soil stack is fine. Your problem is local in the second floor sink. Good luck, Tom