The Sch\"{o}nberg-Chandrasekhar limit in post main sequence evolution for
stars of masses in the range $1.4\lesssim M/{M}_{\odot}\lesssim 6$ gives the
maximum pressure that the stellar core can withstand, once the central hydrogen
is exhausted. It is usually expressed as a quadratic function of $1/\alpha $ ,
with $\alpha $ being the ratio of the mean molecular weight of the core to that
of the envelope. Here, we revisit this limit in scenarios where the pressure
balance equation in the stellar interior may be modified, and in the presence
of small stellar pressure anisotropy, that might arise due to several physical
phenomena. Using numerical analysis, we derive a three parameter dependent
master formula for the limit, and discuss various physical consequences. As a
byproduct, in a limiting case of our formula, we find that in the standard
Newtonian framework, the Sch\"{o}nberg-Chandrasekhar limit is best fitted by a
polynomial that is linear, rather than quadratic, to lowest order in
$1/\alpha $ .