Traffic-responsive signal control is a cost-effective, easy-to-implement, network management strategy, bearing high potential to improve performance in heavily congested networks with dy-namic traffic characteristics. Max Pressure (MP) distributed control gained significant popularity due to its theoretically proven ability of throughput maximization under specific assumptions. However, its effectiveness is questionable in over-saturated conditions, while network-scale implementation is often practically limited due to high instrumentation cost, which increases proportionally to the number of controlled intersections. Perimeter control (PC) based on the concept of Macroscopic Fundamental Diagram (MFD) is a state-of-the-art aggregated control strategy that regulates exchange flows between homogeneously congested regions, with the objective of maximizing traffic system performance and prevent over-saturation. However, homogeneity assumption is hardly realistic under congested conditions, which can compromise PC effectiveness. In this paper, network-wide parallel application of PC and MP strategies embedded in a two-layer control framework is evaluated in a macroscopic simulation environment. With the aim of reducing implementation cost of network-wide MP without significant performance drop, we propose a critical node identification algorithm that is based on node traffic characteristics and assess partial MP deployment to the most critical nodes. An enhanced version of Store-and-forward dynamic traffic paradigm incorporating finite queues and spill-back consideration is used to test different configurations of the two-layer framework, as well as each layer individually, for a real large-scale network, in moderate and highly congested conditions. Results show that: (i) combination of MP and PC outperforms individual layer application in almost all cases for both demand scenarios tested; (ii) MP control in critical node sets formed by the proposed strategy leads to similar or even better performance compared to full-network implementation, thus allowing for significant cost reduction; iii) the proposed control schemes improve system performance even under stochastic demand fluctuations of up to 20% of mean.