Basement Plumbing Rough-in drawing
There are many different ways to do this, no one particular piping configuration is the only way, there are probably 10 different ways to pipe up this bathroom. This is just one option you have based on existing pipe routing and assumed elevations you may encounter when you remove the slab. So with that said, depending on how deep your existing 4" line is under the slab you might be limited to how far you can run. If you look at the attached PDF, I suggest running a 3" trunk line parrallel to the existing 4" line from that point all the way to a new cleanout next to the sink. When you connect into the 4" line you need to be a minimum of 40 inches downstream of the stack to avoid the hydraulic jump that occures when the stack goes horizontal. The 3" line will also allow you to pitch a 1/8" per foot all the way to the sink. Once you go smaller than a 3", you are required to pitch at 1/4" per foot. This should allow you to run the piping hopefully without having to cast the pipe in the new floor slab since the elevation at the end of the run may be slightly higher than the 4" where it goes horizontal. For the venting, I think you can use a circuit vent, which is a vent tap off the line after the first fixture, and after the last fixture instead of venting each individual fixture (easier install, same number of vents). For the washing machine, just provide a 2" trap and run a 2" line above the floor and connect into the 2" sink drain (which should also be vented) before it goes through the slab. No piping under the slab should be less than 2" in diameter (good engineering practice). Also, the existing floor drain pipe might be in the way when you run the 3" line, if so you will have to re-connect the floor drain pipe somehow depending on how its currently configured under the floor.
Disclaimer: In no way is this advice and drawing schematic considered 100% accurate or complete, you should obtian the advice of a licensed professional in your state and have the piping installed in conformance with your local rules and regulations.