  We study three aspects of the early-evolutionary phases in low-mass stars
within Eddington-inspired Born-Infeld (EiBI) gravity, a viable extension of
General Relativity. These aspects are concerned with the Hayashi tracks (i.e.
the effective temperature-luminosity relation); the minimum mass required to
belong to the main sequence; and the maximum mass allowed for a fully
convective star within the main sequence. In all cases we find a dependence of
these quantities not only on the theory's parameter, but also on the star's
central density, a feature previously found in Palatini $f(R)$ gravity. Using
this, we investigate the evolution of these quantities with the (sign of the)
EiBI parameter, finding a shift in the Hayashi tracks in opposite directions in
the positive/negative branches of it, and an increase (decrease) for positive
(negative) parameter in the two masses above. We use these results to
ellaborate on the chances to seek for traces of new physics in low-mass stars
within this theory.
