In this paper, we present multi-almost periodicity of a general class of discrete-time neural networks derived from a well-known semi-discretization technique, that is, coexistence and exponential stability of 2N almost periodic sequence solutions of discrete-time neural networks subjected to external almost periodic stimuli. By using monotonicity and boundedness of activation functions, we construct 2N close regions to attain the existence of almost periodic sequence solutions. Meanwhile, some new and simple criteria are derived for the networks to converge exponentially toward 2 N almost periodic sequence solutions. As special cases, our results can extend to discrete-time analogues of periodic or autonomous neural networks and hence complement or improve corresponding existing ones. Finally, computer numerical simulations are performed to illustrate multi-almost periodicity of semi-discretizations of neural networks.