Emerging concepts from scientific deep machine learning such as physics-informed neural networks (PINNs) enable a data-driven approach for the study of complex kinetic problems. We present an extended framework that combines the advantages of PINNs with the detailed consideration of experimental parameter variations for the simulation and prediction of chemical reaction kinetics. The approach is based on truncated Taylor series expansions for the underlying fundamental equations, whereby the external variations can be interpreted as perturbations of the kinetic parameters. Accordingly, our method allows for an efficient consideration of experimental parameter settings and their influence on the concentration profiles and reaction kinetics. A particular advantage of our approach, in addition to the consideration of univariate and multivariate parameter variations, is the robust model-based exploration of the parameter space to determine optimal reaction conditions in combination with advanced reaction insights. The benefits of this concept are demonstrated for higher-order chemical reactions including catalytic and oscillatory systems in combination with small amounts of training data. All predicted values show a high level of accuracy, demonstrating the broad applicability and flexibility of our approach.