Does time dilation increase within overlapping gravitational fields?
Gravitational time dilation depends on the observers' relative positions in the gravitational potential.

For relatively weak gravitational fields the rate at which a clock ticks for observer A compared to the clock rate for observer B is given by
$$\frac{d \tau_{\rm A}}{d\tau_{\rm B}} \simeq \sqrt{1 + \frac{2\Delta \Phi_{\rm AB}}{c^2}} \sim 1 + \frac{\Delta \Phi_{\rm AB}}{c^2},$$
where $\Delta \Phi_{\rm AB}$ is the difference in gravitational potential between observers A and B.

Gravitational potential is a scalar quantity, so the basic answer to your question is yes - the effects of the two neutron stars would be summative. However, I would hesitate to use the approximation above when dealing with the strong gravity near neutron stars.