Stroke is a leading cause of adult disability that results in motor deficits and reduced independence. Regaining independence relies on motor recovery, particularly regaining function of the hand and arm. This review presents evidence from human studies that have used transcranial magnetic stimulation (TMS) to identify neurophysiological mechanisms underlying upper limb motor recovery early after stroke. TMS studies undertaken at the subacute stage after stroke have identified several neurophysiological factors that can drive motor impairment, including membrane excitability, the recruitment of corticomotor neurons, and glutamatergic and GABAergic neurotransmission. However, the inherent variability and subsequent poor reliability of measures derived from motor evoked potentials (MEPs) limit the use of TMS for prognosis at the individual patient level. Currently, prediction tools that provide the most accurate information about upper limb motor outcomes for individual patients early after stroke combine clinical measures with a simple neurophysiological biomarker based on MEP presence or absence, i.e. MEP status. Here, we propose a new compositional framework to examine MEPs across several upper limb muscles within a threshold matrix. The matrix can provide a more comprehensive view of corticomotor function and recovery after stroke by quantifying the evolution of subthreshold and suprathreshold MEPs through compositional analyses. Our contention is that subthreshold responses might be the most sensitive to reduced output of corticomotor neurons, desynchronized firing of the remaining neurons, and myelination processes that occur early after stroke. Quantifying subthreshold responses might provide new insights into post-stroke neurophysiology and improve the accuracy of prediction of upper limb motor outcomes.