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 that have diverse types of QoS profiles and/or traffic patterns and which originate 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. The spreading of MOMA is able to provide various interference pattern, while on the other hand the flexible receiver structure allows to concentrate the receiver complexity where effectively needed. Practical implementations of the MOMA principle are provided for base stations (BS) that are equipped with a large number of antenna elements along with a discussion of the associated receiver structure. It is shown that such a massive-multiple-inputmultiple-output (MIMO) scenario enables the achievement of all the benefits of MOMA even with relatively receiver structure.