Chemical Exchange Saturation Transfer (CEST) imaging is a promising MRI molecular imaging technique that allows for multiple parameter quantification (MPQ) of various molecules. However, the presence of overlapping confounding signals and poor data quality pose challenges in accurately quantifying the CEST effect and the underlying exchange parameters. In this paper, we propose a deconvolution-based preprocessing and a deep learning architecture called Deep Multiple Z-spectrum Quantification (DMUZQ) to address these limitations and enable automatic MPQ in CEST imaging. Our approach begins with a deconvolution kernel that minimizes interference from overlapping pools in CEST Z-spectra. This preprocessing step enhances the features of the solute of interest and improves data quality, enabling more specific molecular information to be extracted. The DMUZQ model utilizes multiple power level signals and provides a weighted average of the quantified outcome, leading to enhanced accuracy and robustness in parameter quantification. We perform model optimization at both the individual and complete model levels. To estimate the accurate range of solute exchange rate, we introduce explicit regularization using the Lyapunov stability criteria, which considers the functional relationship between solute concentration, relaxation time, and exchange rate. We validate the DMUZQ model through comprehensive analysis and comparisons with existing deep learning models, variants, and a conventional CEST quantification method based on data fitting. Simulated data experiments demonstrate that our DMUZQ method achieves higher accuracy when compared to ground truth. Evaluation on animal tumor models further confirms its superior performance over the conventional fitting approach.