This paper proposes a new random access Medium Access Control (MAC) protocol, named as Full-duplex Mul- tipacket reception Medium Access Control (FM-MAC), which jointly uses In-band Full-Duplex (FDX) and MultiPacket Recep- tion (MPR) techniques. The protocol was designed to maximize the spectral efficiency by combining the FDX doubling potential and the MPR capability to handle interference due to concurrent transmissions. A cross-layer approach was followed: FM-MAC selects the transmission mode and defines the transmission power to maximize throughput, guaranteeing a minimal bandwidth for mobile terminals (MTs) that cannot use FDX. The performance was evaluated using simulations with 10 MTs, which studied the influence of the load in different combinations of FDX and half- duplex (HDX) MTs. The results show that replacing HDX MTs for FDX increases the throughput 33% and reduces the delay, as long as, the system does not enter into saturation.