By the way it is drawn it is not correctly plumbed. If you seperate the lav from the stack and tie it into w.c. blg drain you could with appropriate sizing wet vent bathroom group. The lav eventually being your wet vent. After tee above floor ties in lav waste you can run vent to attic and tie into exsisting vent. Size's vary on what code you follow, IPC,UPC, or your own state code.