1939 plumbing tie in

I would like to get advice on adding additional bathroom utilizing the existing waste and vent stack. The photo shows what is currently routed into the stack. I would be adding shower, lavatory and toilet. Location of new bathroom is the next room over, about 6 feet to closet fixture.

Cut in a 3" wye under the fitting in the stack, the vents will have to tie in 6" higher then the flood level of the highest fixture on the next floor.

the additional bathroom would be on the same floor, the photo of the stack is located in the basement?

That is definitely 1930's plumbing, and it appears to have been "updated" with some PVC, but if the new piping was done exactly like the old, there may not be any vents for the tub/shower, or lavatory. What is there has no bearing on what you have to do for the new bath. Once you cut a fitting into the existing riser below the other fittings, your will run the piping to the new location and install a completely separate and proper drainage DWV system.

As HJ says, you will need a vent. Are you going to be completely gutting the room that is to become the new bath? If you have the walls open anyway, running the vent upwards would not be a problem. The floor above this picture is the main floor, yes? What is above that? If it is an attic and accessible, you will be able to run your vent alright. If it is finished, consider what you would have to open up if you were to run the vent upwards through that. If the walls in your existing bath are opened up you may find a vent you can tie your new vents into. If there is nothing draining into your stack above your main floor (no fixtures on a second or third level) you might be able to revent back into the stack.

You have a fairly complex job on your hands. Consider hiring it done.