A direct search for electroweak production of charginos and neutralinos is presented. Events with three or four leptons, with up to two hadronically decaying $τ$ leptons, or two same-sign light leptons are analyzed. The data sample consists of 137 fb$^{-1}$ of proton-proton collisions with a center of mass energy of 13 TeV, recorded with the CMS detector at the LHC. The results are interpreted in terms of several simplified models. These represent a broad range of production and decay scenarios for charginos and neutralinos. A parametric neural network is used to target several of the models with large backgrounds. In addition, results using orthogonal search regions are provided for all the models, simplifying alternative theoretical interpretations of the results. Depending on the model hypotheses, charginos and neutralinos with masses up to values between 300 and 1450 GeV are excluded at 95% confidence level.