One of the key requirements for fifth-generation (5G) cellular networks is their ability to handle densely connected devices with different quality of service (QoS) requirements. In this article, we present multi-service oriented multiple access (MOMA), an integrated access scheme for massive connections with diverse QoS profiles and/or traffic patterns originating from both handheld devices and machine-to-machine (M2M) transmissions. MOMA is based on a) establishing separate classes of users based on relevant criteria that go beyond the simple handheld/M2M split, b) class dependent hierarchical spreading of the data signal and c) a mix of multiuser and single-user detection schemes at the receiver. Practical implementations of the MOMA principle are provided for base stations (BSs) that are equipped with a large number of antenna elements. Finally, it is shown that such a massive-multiple-input-multiple-output (MIMO) scenario enables the achievement of all the benefits of MOMA even with a simple receiver structure that allows to concentrate the receiver complexity where effectively needed.