  We analyze the dependence of the chiral phase transition temperature on
baryon number and strangeness chemical potentials by calculating the leading
order curvature coefficients in the light and strange quark flavor basis as
well as in the conserved charge ($B, S$) basis. Making use of scaling
properties of the magnetic equation of state (MEoS) and including diagonal as
well as off-diagonal contributions in the expansion of the energy-like scaling
variable that enters the parametrization of the MEoS, allows to explore the
variation of $T_c(\mu_B,\mu_S) = T_c ( 1 - (\kappa_2^B \hat{\mu}_B^2 +
\kappa_2^S \hat{\mu}_S^2 + 2\kappa_{11}^{BS} \hat{\mu}_B \hat{\mu}_S))$ along
different lines in the $(\mu_B,\mu_S)$ plane. On lattices with fixed cut-off in
units of temperature, $aT=1/8$, we find $\kappa_2^B=0.015(1)$,
$\kappa_2^S=0.0124(5)$ and $\kappa_{11}^{BS}=-0.0050(7)$. We show that the
chemical potential dependence along the line of vanishing strangeness chemical
potential is about 10\% larger than along the strangeness neutral line. The
latter differs only by about $3\%$ from the curvature on a line of vanishing
strange quark chemical potential, $\mu_s=0$. We also show that close to the
chiral limit the strange quark mass contributes like an energy-like variable in
scaling relations for pseudo-critical temperatures. The chiral phase transition
temperature decreases with decreasing strange quark mass, $T_c(m_s)=
T_c(m_s^{\rm phy}) (1 - 0.097(2) (m_s-m_s^{\rm phys})/m_s^{\rm phy}+{\cal
O}((\Delta m_s)^2)$.
