The ability of mobility management to provide seamless communication and better quality of service (QoS) to the multiservice multimode mobile node (MMMN), which can run multiple services simultaneously during roaming in ultra-dense heterogeneous networks with different radio access technologies, is a major challenge in implementing 5G and beyond. Ultra-dense heterogeneous networks (HetNet), restrictions on multiservice multimode mobile terminals, and user mobility all lead to a number of serious problems, such as the ping-pong effect, unnecessary handovers, and decreasing cell edge spectral efficiency. The dense deployment of small base stations also causes a high probability of frequent handovers in HetNet, which has led to a significant escalation in energy consumption resulting from unnecessary signaling, increased network overhead, and higher energy usage by network equipment. This increased energy requirement may lead to potentially increase the emissions of greenhouse gases to meet the energy production needs. Several handover decision algorithms have been proposed, but most of them deal with only running a single service at a time on a mobile node. In this paper, authors propose a new network selection model for MMMN which may run multiple services simultaneously. This model uses context-aware information about the user’s preferences, characteristics, and needs of the services, limitations of mobile terminal, and network conditions of an ultra-dense HetNet to choose the best network. The fundamental principle of this model is based on the comprehensive network criteria weight computed by the integration of Enhanced CRiteria Importance Through Inter-criteria Correlation (CRITIC), fuzzy analytic hierarchy process (FAHP), and group decision-making (GDM) techniques and the service priority of running services. For computing the objective weight of criteria, a novel improved CRITIC method has been proposed. At the same time, sigmoid utility functions and linear utility functions have been used to figure out the value of network criteria for running multiple services on the mobile node. Finally, the best network from HetNet for MMMN is selected using the technique for order performance by similarity to ideal solution (TOPSIS) and threshold by computing a comprehensive utility value network criteria decision matrix and comprehensive network criteria weight. The simulation results show that the proposed model increases the selection probabilities of an appropriate network according to the service requirements and network conditions. It also reduces unnecessary handovers and improves QoS while satisfying users’ preferences, service requirements, and terminal constraints, in solving the MMMN network selection problem.