Batn reno venting question

I am installing a new 3 piece bath in the basement as part of a remodel of a formally empty basement. Currently there is an unused roughin for a toilet. I plan to break up the floor and switch this to a shower drain. Then I will install a toilet and sink with vanity.

My dilemia is the following:Originally I thought I would need another stack to vent the fixtures but the only place to get a vertical run to the roof is approximately five feet further from the planned fixtures than the current 3" cast iron stack.

My question is twofold, 1) will the current stack suffice as the vent for these fixtures and 2) should the drain for the sink be upstream from the new toilet?

Comments would be appreciated, a small drawing of the current and proposed set up is attached

Thanks Gerry

Each of the fixtures needs to be vented, but that doesn't mean you need 3 runs to the attic. But, is that one line going up a drain for the first floor? If so, then it isn't suitable for a vent for your basement bathroom; at least not unless you can run a vent up above the highest flood plane (in other words, connect into it where it is no longer a drain, but a vent). All of the three fixtures can be joined together so you only need one line going up. based on the diameter of the pipe, that determines how far it can be from the vent, but you should not run a drain past another's trap without venting it first.

Bath reno

Then its looks like I am back to my first thoughts. Start new 3"vent from new toilet run this vertical up the wall behind new toilet to the ceiling then horizontal in the basement ceiling for the 8 to 9 feet then verticle up thru roof thru a closet on the main floor. Then run 2"vent line from shower and 1 1/2 vent line from sink connecting these to the new 3" vent line horizontally in the basement ceiling just over top the toilet.

How does that sound?

I can't get into existing stack above flood level of upperfloor fixtures.

Vents, like drains, need slope so if any condensation or rainwater get in there, it will drain out, so take that into consideration.