One major knowledge gap in systems biology is the quantification of dynamic protein synthesis rates in response to cell perturbation. To address this gap, we have developed MITNCAT, multiplex isotope tagging / non-canonical amino acid tagging, a novel method enabling the robust quantification of proteome-wide protein synthesis rates with high temporal resolution (15-30 minutes) across multiple time points or treatment conditions, in a single analysis. MITNCAT combines multiplexed isobaric mass tagging with bioorthogonal non-canonical amino acid tagging (BONCAT) to label newly synthesized proteins with azidohomoalanine (Aha) and pulsed SILAC (pSILAC), thus providing enrichment and multiplexed quantification of newly synthesized proteins. We demonstrate the application of MITNCAT to quantify altered protein synthesis rates following induction of the unfolded protein response (UPR) and epidermal growth factor (EGF) stimulation. Eliciting the UPR by blocking N-glycosylation results in a global down-regulation of protein synthesis, with stronger down-regulation of proteins involved in the glycolysis pathway and protein synthesis machinery (ribosomal proteins, initiation factors, and elongation factors), but up-regulation of several key protein-folding chaperones. MITNCAT enables the quantification of waves of temporally distinct protein synthesis in response to EGF stimulation, with altered protein synthesis on dozens of proteins detectable in the first 15 minutes. Comparison of protein synthesis with RNA sequencing and ribosome footprinting allowed the distinction between protein synthesis driven by an increase in transcription versus that driven by an increase in translational efficiency. Temporal delays between ribosome occupancy and protein synthesis were observed and found to correlate with altered codon usage in significantly delayed proteins.