1. You CANNOT connect to the 3" stack on the left
2. You are assuming that after you change the riser to 2", which would be necessary, that the 2" horizontal drain in the basement will be adequate for the flow.
3. Your washer trap tee will have to be below the tee for the sink on the other side.
4. You will have to insure that the height of the washer drain standpipe, does not exceed the maximum permitted by your code. Usually 24" to 30" above the trap.
5. Requirements #3 and #4 may be mutually exclusive so that you cannot do BOTH.