Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this formulation is applicable in these domains. We study the complexity of the general problem, and a variant of it where preprocessing is allowed. We show that when the parametric weights are linear functions, algorithms remain tractable even under our relaxed assumptions. Furthermore, we show that if the weights are allowed to be nonlinear, the problem becomes NP-hard. We also study the multi-dimensional version of the problem where the weight functions are parameterized by multiple parameters. We show that even with 2 parameters, this problem is NP-hard. © 2021 37th Conference on Uncertainty in Artificial Intelligence, UAI 2021. All Rights Reserved.