HI MIKE,
I APOLOGIZE FOR THE DELAY BUT I NEEDED TIME TO STUDY AND RESEARCH YOUR PREPOSAL. I'M GOING TO USE A LITTLE DIFFERENT FORMAT IN ANSWERING. I'LL EDIT YOUR POST AND ANSWER IN CAPS.

I was getting ready to finish my basement and plan to install a 1/2 bath myself (toilet and lavatory). My plan is to tie into an existing 3" stack from my first floor masterbath. Currently the 3" stack enters through the concrete and then has a long 90 which runs to the main waste line (lines runs perpendicular and away from the wall I plan to install the lavatory and toilet. My plan is to cut out the existing Long 3" 90 and replace with a 3" Wye fitted with a 3" street 45 (to connect to the existing 3" stack). MOST CODES CALL FOR 4" UNDER THE CEMENT. I will then use the other side of the 3" Wye fitting to install a 3x3x2 Tee and run a 3" long 90 to a flange for the toilet. For the 2" portion of the Tee I intend to angle it at approximately 45 degrees so it points upwards to the lavatory. I will then run the necessary pipe and fittings to get above the concrete and in the wall that will be there to the necessary stub out. WHY WOULD YOU WISH TO BRING THE DRAINAGE ABOVE GRADE? From there I will insert a 2x2x1.5 Tee that will run into the joist of my subfloor where I have approximately 12" to tie into the existing 1.5" vent which runs out the roof. Since I'm tying into an existing stack I was considering using flexible rubber fittings AND HERE IS WHERE I HAD TO RESEARCH FERNCO FITTINGS AND COUPLINGS. I ADVISE AGAINST USING RUBBER FITTINGS OR COUPLINGS IN PLUMBING UNLESS NOTHING ELSE IS AVAILABLE. THE REASON IS THE EXTRA LABOR INVOLVED IN STRAPPING UP THE PIPES IN THE WALL AND HAVING TO BLOCK UP THE PIPES UNDER THE CEMENT SO THEY WILL NOT SAG AND PRESENT A PROBLEM. IS THERE A COMPELLING REASON THAT YOU AREN'T USING CONVENTUAL FITTINGS? For my 1.5 x 1.5 x 1.5 Tee I will need to tie into my existing vent and also using a 3" coupling somewhere below the stack clean out and above the existing concrete to allow for easier installation. The other thing I'm not sure about is if I need a backwater valve. I've read that if the top of any fixture resides below the nearest upstream sewer access point that a backwater valve is needed. My first floor of my house sits approximately 5-7 ft above street level and from what I can tell is that the nearest sewer access is at that same level. Therefore I would assume my toilet is ~1-3 ft below the sewer access point. IF YOUR TOILET'S LOCATED ONE TO THREE FEET BELOW THE MAIN ALL THE CHECK VALVES IN THE WORLD WON'T ALLOW IT TO FLUSH UP HILL If it is needed, can I install it on the opposite side of my 3" stack (due to space constraints) which will mean my downstairs bath and upstairs master would both run through it. Also, I assume if it is below my basement concrete I need to leave access to it somehow in case of any mechanical failures. IT'S A PRUDENT IDEA TO INSTALL CLEANOUTS WHEREVER POSSIBLE. Is there any easy way to test the plumbing once roughed into existing line (doesn't seem like there is any easy way to do a air test or water test because of the existing plumbing in place)? YES THERE IS. AT THE SAME TIME YOU CUT INTO THE MAIN FOR THE BRANCH YOU CAN INSTALL A CLEAN OUT. AS YOU STUB UP THE 4" FOR THE TOILET AND THE 1 1/2" FOR THE LAVATORY GLUE TEST CAPS ON THEM. PUT A INFLATABLE TEST BALL IN THE MAIN TO BLOCK IT OFF AND FILL FROM THE LAVATORY VENT Until IT STARTS TO COME OUT THE FIRST FLOOR TUB OR SHOWER. YOU MAY NOW CHECK THE JOINTS FOR LEAKS.

Also, I want to install a wetbar on the opposite side of the basement. I plan to tie it into a 3" waste stack which has my kitchen and washer on it. The run will be about 15 ft. I plan to use 2" pipe and again tie in with a 3x3x2 flexbible rubber fitting. I do not have any easy way to dry vent this since the vents are somewhere in my first floor interior wall, instead my plan was to use an Air Admittance Valve and install near the ceiling in the basement where if I needed to I could access through the drop ceiling.
IF CODE ALLOWS THE AAV WORKS FOR ME.
Sorry for being a long, but I wanted to be as clear as possible to minimize any confusion. Please advise if what I stated above will work, meets code, and is the proper way to do it.
LET ME KNOW YOUR THOUGHTS. REGARDS, TOM
Thanks for your help

This post is just to get your question up on top and to let you know that you've been answered. Cheers, Tom

Thanks Tom, Below are responses to your statements and further clarify

You stated "MOST CODES CALL FOR 4" UNDER THE CEMENT", to further clarify the stack that I want to tie into is not the main stack. It is a 3" stack that runs vertically to the basement floor and makes a 90 degree turn and runs for about 10' to the 4" main line.

I plan to put my basement wall close to the 3" stack (which has my master bath on it; toilet, shower, tub, dbl lavatory) and install my stool and lavatory on the same wall.

What I wanted to do and mentioned above, I'll call option 1.
Option 1 - Replace the existing 90 with a Wye/45 combo to tie the existing stack and horizontal run back together and from there run out ~15" to where I will install the center of my flange flush with the basement floor (this will leave me about 13" from the center of the flange to the edge of the finished wall). Between my closet elbow and the other end of the Wye it connects into I was planning to install a 3x3x2 T where the T will be angled such that the 2" hole will angled 45 degrees above the grade plane. I wanted to use this to wet vent the toilet and tie in the lavatory drain. However, I don't think laying a T horizontally for drainage is acceptable and that would lead into option 2.

Option 2 - Do everything as mentioned above except use the 3x3x2 for dry venting toilet only. For the toilet vent, I could remove more concrete on the downstream side of the existing 3" horizontal run. From there I would install another Wye with either a 1.5" or 2" to drain my lavatory. Then above the lavatory I would tie the two separate vents together and then tie into the existing 1.5" vent at the first floor joist level.

Option 3 - Cut about 10' to 15' of concrete and tie into the existing 4" main and either tie into existing venting or run new venting through the 1st floor wall and attic. I hope I don't have to do this option.

I main questions which apply to most of these options are:

1) Can I tie into the existing 1.5" vent for my basement toilet and lavatory (I think it currently only vents the 1st floor toilet and shower, the dbl vanity and tub are vented separately in the 1st floor walls and run to the attic where they all tie in together)?

2) Which option should I go with? or do you have a 4th option that may work better?

3) You mentioned 4" flange above. Should I use a 4x3" flange or standard 3" flange if I tie into a 3" pipe?

4) Should I install a cleanout in the horizontal 3" line under the concrete downstream of all the new fixtures that will be added? As you mention above for the water test. Seems like it would be nice to have for that purpose.

Regarding your comment about rubber fittings, I thought I may need to use them to tie into existing piping to make installation easier, but it sounds like I shouldn't have any problems with standard PVC fittings. I assume once I cut the existing pipes there will be some flexibility to allow me to tie in.

Again thanks for the help. Hopefully I clarified things a little better above.

Mike I got your E mail. A thousand pardons! You got lost in traffic and buried. Let's take option one;

Option 1 - Replace the existing 90 with a Wye/45 combo to tie the existing stack and horizontal run back together and from there run out ~15" to where I will install the center of my flange flush with the basement floor (this will leave me about 13" from the center of the flange to the edge of the finished wall). Between my closet elbow and the other end of the Wye it connects into I was planning to install a 3x3x2 T where the T will be angled such that the 2" hole will angled 45 degrees above the grade plane. I wanted to use this to wet vent the toilet and tie in the lavatory drain. However, I don't think laying a T horizontally for drainage is acceptable and that would lead into option 2.
THE 3X3X2" TEE WILL LAY HORIZONTALLY WITH A LITTLE PITCH. NO NEED TO SLANT IT UP 45 DEGREES.

1) Can I tie into the existing 1.5" vent for my basement toilet and lavatory (I think it currently only vents the 1st floor toilet and shower, the dbl vanity and tub are vented separately in the 1st floor walls and run to the attic where they all tie in together)?
YOU MAY REVENT BACK TO THE 1st. FLOOR VENT ONLY IF IT'S A DRY VENT UPWARDS FROM THE TIE IN POINT.
2) Which option should I go with? or do you have a 4th option that may work better?
i WOULD GO WITH OPTION NUMBER ONE. IT SOUNDS LIKE THE EASIEST ONE TO WORK WITH
3) You mentioned 4" flange above. Should I use a 4x3" flange or standard 3" flange if I tie into a 3" pipe?
A REGULAR 3" FLANGE WILL DO.
4) Should I install a cleanout in the horizontal 3" line under the concrete downstream of all the new fixtures that will be added? As you mention above for the water test. Seems like it would be nice to have for that purpose.
AT THE SAME TIME YOU CUT INTO THE MAIN FOR THE BRANCH YOU CAN INSTALL A CLEAN OUT. AS YOU STUB UP THE 4" FOR THE TOILET AND THE 1 1/2" FOR THE LAVATORY GLUE TEST CAPS ON THEM. PUT A INFLATABLE TEST BALL IN THE MAIN TO BLOCK IT OFF AND FILL FROM THE LAVATORY VENT Until IT STARTS TO COME OUT THE FIRST FLOOR TUB OR SHOWER. YOU MAY NOW CHECK THE JOINTS FOR LEAKS.
Regarding your comment about rubber fittings, I thought I may need to use them to tie into existing piping to make installation easier, but it sounds like I shouldn't have any problems with standard PVC fittings. I assume once I cut the existing pipes there will be some flexibility to allow me to tie in.
IF THE PIPES ARE RIDGED AND CAN'T BE MOVED I USE NO-HUB COUPLINGS,(SEE IMAGE) TO CONNECT THE FITTINGS. UNLIKE FERNCO RUBBER COUPLINGS NO-HUB COUPLINGS WILL SUPPORT THE JOINT AND NOT ALLOW IT TO SAG CAUSING PROBLEMS.
GOOD LUCK, TOM