Extended T-N Plane Abstraction (E-TNPA) proposed in this paper realizes work-conserving and efficient optimal real-time scheduling on multiprocessors relative to the original T-N Plane Abstraction (TNPA). Additionally a scheduling algorithm named NVNLF (No Virtual Nodal Laxity First) is presented for E-TNPA. E-TNPA and NVNLF relax the restrictions of TNPA and the traditional algorithm LNREF, respectively. Arbitrary tasks can be preferentially executed by both tie-breaking rules and time apportionment policies in accordance with various system requirements with several restrictions. Simulation results show that E-TNPA significantly reduces the number of task preemptions as compared to TNPA.