T cells can recognize a few molecules of cognate antigen amongst vastly outnumbering non-cognate ligands. The T cell receptor (TCR) differentiates antigens based on antigen-TCR binding dwell time through a kinetic proofreading process. Historically, this has been modeled as the ligated receptor undergoing a series of reactions before producing a signal. In such a sequential mechanism, the number of steps is a key determinant of discrimination fidelity. Here, we consider two features of the molecular mechanism of TCR activation that diverge from a sequential process and suggest that an alternative kinetic proofreading mechanism may be at play. First, activation processes of multiple ITAM domains of the TCR represent parallel reaction sequences taking place on a single TCR molecule. Second, the states of the parallel proofreading reactions are integrated to produce a binary output from each TCR in the form of a discrete LAT condensation event, which may or may not occur. We examine a revised kinetic proofreading scheme based on parallel reactions followed by an integration step (multi-thread scheme) and compare its performance with the sequential scheme in a stochastic setting. A distinct difference in a multi-thread scheme is that multiplicity of the parallel reaction threads provides an additional means to increase discrimination fidelity. This relieves the need for fine-tuned kinetics among chemically distinct reaction steps, which is a major hurdle for physical implementation of a sequential mechanism. Lastly, we reinterpret previously reported experimental observations and find that various proofreading behaviors are well described as proofreading through parallel reaction threads.