Fluorescence-based single-molecule and fluctuation spectroscopy in the near-IR can open avenues for biomolecular dynamic studies in biological media with suppressed autofluorescence and scattering background. However, further implementation is limited by the lower brightness of NIR fluorophores and available single-photon detector technologies that are still to be explored and adapted. Superconducting nanowire single-photon detectors (snSPDs) have found increasing use in quantum optics and optical communication applications thanks to high sensitivity in the near-infraed (NIR), low dark-counts, no after-pulsing, and high time resolution. Here, we present characterization of fluorescence intensity fluctuations from single vesicles and NIR fluorophores based on fluorescence correlation spectroscopy (FCS), specifically taking advantage of these snSPD properties. We present a concept allowing multiplexed readouts based on only one snSPD, in which the emitted photons are separated by their emission wavelength into different optical paths, thereby translating the emission wavelengths into different arrival times onto the snSPD. This concept allows one-laser-one-detector, dual-color fluorescence cross-correlation spectroscopy (FCCS) measurements, with fluorescence intensity fluctuations of two fluorophore species separately analyzed and cross-correlated. It is shown how two fluorophore species in a sample can be distinguished by their different blinking kinetics, fluorescence lifetimes, and/or diffusion properties. Apart from differences in emission spectra, the presented concept for multiplexing using a single detector can also be applied to distinguish emitters by properties such as polarization, coherence lengths, and fluorescence bunching and antibunching signatures. It can also be generalized to other modalities than FCS, including single-molecule detection, confocal microscopy, and imaging.