Synthetic magnetic resonance spectra (MRS) are mathematically generated spectra which can be used to investigate the assumptions of data analysis strategies, optimize experimental design, and as training data for the development and validation of machine learning tools. In this work, we extend Magnetic Resonance Spectrum Simulator (MARSS), a popular MRS basis set simulation tool, to be able to generate synthetic spectra for an arbitrary MRS sequence. The extension, referred to as synMARSS, converts a basis set as well as a set of NMR, tissue-related and additional sequence parameters into high-quality synthetic spectra via a parametric model. synMARSS is highly versatile, incorporating T1 and T2 relaxation, arbitrary line shape distortions and diffusion, while also quickly generating the large amount of training data needed for machine learning applications. Additionally, we extend MARSS to non-1H nuclei, such as 2H, 13C, and 31P. We use synthetic spectra to investigate the effects of approximating 14N heteronuclear coupling as weak homonuclear coupling, which was found to have small effects on the quantified concentrations for major metabolites for the implementation of PRESS at short echo time, but these effects increased at longer echo times.