Given a signaling network, the target combination identification problem aims to predict efficacious and safe target combinations for treatment of a disease. State-of-the-art in silico methods use Monte Carlo simulated annealing (mcsa) to modify a candidate solution stochastically, and use the Metropolis criterion to accept or reject the proposed modifications. However, such stochastic modifications ignore the impact of the choice of targets and their activities on the combination's therapeutic effect and off-target effects which directly affect the solution quality. In this paper, we present Steroid, a novel method that addresses this limitation by leveraging two additional heuristic criteria to minimize off-target effects and achieve synergy for candidate modification. Specifically, off-target effects measure the unintended response of a signaling network to the target combination and is generally associated with toxicity. Synergy occurs when a pair of targets exerts effects that are greater than the sum of their individual effects, and is generally a beneficial strategy for maximizing effect while minimizing toxicity. Our empirical study on the cancer-related mapk-pi3k network demonstrates the superiority of Steroid in comparison to mcsa-based approaches. Specifically, Steroid is an order of magnitude faster and yet yields biologically relevant synergistic target combinations with significantly lower off-target effects.