In quantitative proteomics, mass tag labeling techniques have been widely adopted in mass spectrometry experiments. These techniques allow peptides and proteins from multiple samples of a batch being quantified in a single experiment, and as such greatly improve the efficiency of protein profiling. However, the batch-processing of samples also results in severe batch effects and non-ignorable missing data occurring at the batch level. Motivated by the breast cancer proteomic data from the Clinical Proteomic Tumor Analysis Consortium, in this work, we developed two tailored multivariate MIxed-effects SElection models (mvMISE) to jointly analyze multiple correlated peptides/proteins in labeled proteomics data, considering the batch effects and the non-ignorable missingness. Applying the proposed methods to the motivating data set, we identified phosphoproteins and biological pathways that showed different activity patterns in triple negative breast tumors versus other breast tumors. The proposed methods can also be applied to other high-dimensional multivariate analyses based on clustered data with or without non-ignorable missingness.