Spectroscopy is a popular technique for identifying and quantifying fluorophores in fluorescent materials. However,quantifying the fluorophore of interest can be challenging when the material also contains other fluorophores (baseline), particularly if the emission spectrum of the baseline is not well-defined and overlaps with that of the fluorophore of interest. In this work, we propose a method that is free from any prior assumptions about the baseline by utilizing fluorescence signals at multiple excitation wavelengths. Despite the nonlinearity of the model, a closed-form expression of the least squares estimator is also derived. To evaluate our method, we consider the practical case of estimating the contributions of two forms of protoporphyrin IX (PpIX) in a fluorescence signal. This fluorophore of interest is commonly utilized in neuro-oncology operating rooms to distinguish the boundary between healthy and tumor tissue in a type of brain tumor known as glioma. Using a digital phantom calibrated with clinical and experimental data, we demonstrate that our method is more robust than current state-of-the-art methods for classifying pathological status, particularly when applied to images of simulated clinical gliomas. To account for the high variability in the baseline, we are examining various scenarios and their corresponding outcomes. In particular, it maintains the ability to distinguish between healthy and tumor tissue with an accuracy of up to 87%, while the ability of existing methods drops near 0%.