The synthesis of heat recovery networks traditionally results in an optimal or suboptimal solution for the supplied set of streams and simplifying assumptions. In the current work, the assumption of a single optimal solution is replaced by the goal of generating an ordered set of optimal or quasi-optimal networks. This enables industrial engineers to further select the solution most suitable for detailed design and practical implementation. The problem is formulated for and solved by an extension of the P-graph framework for combinatorial process network optimization. The presented method for HEN synthesis generates a list of solutions ranked by the Total Annualized Cost. In addition to the feasibility, all list elements also feature a degree of heat recovery ranging from the thermodynamic maximum, down to a specified margin allowing accounting for the energy-capital trade-off. The current method is illustrated with three case studies. The obtained results demonstrate optimal solutions that cannot be generated by the Pinch-based methods or the stage-wise superstructure approaches. The proposed parameters, an upper limit on the number of heat exchangers per process stream and a maximum relaxation of utility demand compared to the Pinch targets, allow performing parametric evaluations of the resulting solutions.