In this paper, we address the problem of network design with redundant connections, often faced by operators of telephone and internet services. The network connects customers with one master node and is built by taking into account the rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated $m$ Two-Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated $m$ Ring Star Problem). In this variant of CmRSP, the rings are not constrained to be cycles; instead, they can be two-node connected components. The contributions of this paper are: (a) the introduction and definition of a new problem, (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by the developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work.