A variety of real-world problems are characterized by multimodal functions, i.e., they demand the identification of several locally or globally optimal solutions. In the field of multimodal optimization, researchers actively address the development of niching techniques by inventing new methods and also by coupling existing methods with global optimization metaheuristics. In this paper, we put forward a general niching framework for the Variable Mesh Optimization (VMO) metaheuristic algorithm, coined as Variable Mesh Optimization with Niching (VMO-N). We argue that the basic VMO formulation can be easily adapted to multimodal optimization scenarios without extra adjustments. We refer to the recently published Niche-Clearing-based Variable Mesh Optimization (NC-VMO), as an instantiation of the VMO-N framework proposed here. Since the niche clearing procedure in NC-VMO requires a priori knowledge of the fitness landscape, we also introduce the Niche-based VMO via Adaptive Species Discovery (VMO-ASD) as another instance of VMO-N, in order to show its applicability to a wider range of multimodal problems. VMOASD results with some of the benchmark functions for the CEC'2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization confirm that VMO-N is a plausible general VMO niching framework for multimodal problems. We demonstrate the advantages of VMO-N over the canonical version of the algorithm, VMO-ASD over NC-VMO and also report on VMO-N's performance against other state-of-the-art niching algorithms. Further pursuits of strongly competitive versions of VMO-N will demand the use of more suitable niching methods than both clearing and ASD within the framework although this is not the focal point of this study.