Enhancement or inhibition of cytokine signaling and corresponding immune cells responses are critical factors in various disease treatments. Cytokine signaling may be inhibited by cytokine-neutralizing antibodies (CNAs), which prevents further activation of cytokine receptors. However, CNAs may result in enhanced-instead of inhibitory-cytokine signaling (an "agonistic effect") in various in vitro and in vivo experiments. This may lead to lack of efficacy or adverse events for cytokine-inhibiting based medicines. Alternatively, cytokine-antibody complexes may produce stronger signaling vs. cytokine alone, thereby increasing the efficacy of stimulating cytokine-based drugs, at equal or lower cytokine doses. In this paper, the effect of cytokine signaling enhancement by a CNA was studied in a generic mathematical model of interleukin-4 (IL-4) driven T-cell proliferation. The occurrence of the agonistic effect depends upon the antibody-to-cytokine binding affinity and initial concentrations of antibody and cytokine. Model predictions were in agreement with experimental studies. When the cytokine receptor consists of multiple subunits with substantially differing affinities (e.g., IL-4 case), the choice of the receptor chain to be blocked by the antibody is critical, for the agonistic effect to appear. We propose a generic mechanism for the effect: initially, binding of the CNA to the cytokine reduces free cytokine concentration; yet, cytokine molecules bound within the cytokine-CNA complex-and released later and over time-are "rescued" from earlier clearance via cellular internalization. Hence, although free cytokine-dependent signalling may be less potent initially, it will also be more sustained over time; and given non-linear dynamics, it will lead ultimately to larger cellular effector responses, vs. the same amount of free cytokine in the absence of CNA. We suggest that the proposed mechanism is a generic property of {cytokine, CNA, receptor} triads, both in vitro and in vivo, and can occur in a predictable fashion for a variety of cytokines of the immune system.