  The Co-varying Physical Couplings (CPC) framework is a modified gravity set
up assuming Einstein Field Equations wherein the quantities $\{G,c,\Lambda\}$
are promoted to space-time functions. Bianchi identity and the requirement of
stress-energy tensor conservation entangle the possible variations of the
couplings $\{G,c,\Lambda\}$, which are forced to co-vary as dictated by the
General Constraint (GC). In this paper we explore a cosmological model wherein
$G$, $c$ and $\Lambda$ are functions of the redshift respecting the GC of the
CPC framework. We assume a linear parametrization of $\Lambda$ in terms of the
scale factor $a$. We use the ansatz $\dot{G}/G = \sigma \left( \dot{c}/c
\right)$ with $\sigma =$ constant to deduce the functional forms of $c=c(z)$
and $G=G(z)$. We show that this varying-$\{G,c,\Lambda\}$ model fits SNe Ia
data and $H(z)$ data with $\sigma = 3$. The model parameters can be constrained
to describe dark energy at the background level.
