Territorial Differential Meta-Evolution (TDME) is an efficient, versatile, and reliable algorithm for seeking all the global or desirable local optima of a multivariable function. It employs a progressive niching mechanism to optimize even challenging, high-dimensional functions with multiple global optima and misleading local optima. This paper introduces TDME and uses standard and novel benchmark problems to quantify its advantages over HillVallEA, which is the best-performing algorithm on the standard benchmark suite that has been used by all major multimodal optimization competitions since 2013. TDME matches HillVallEA on that benchmark suite and categorically outperforms it on a more comprehensive suite that better reflects the potential diversity of optimization problems. TDME achieves that performance without any problem-specific parameter tuning.