  We study the evolution of temperature-dependent resistivity with controlled
point-like disorder induced by 2.5 MeV electron irradiation in stoichiometric
compositions of the "3-4-13" stannides,
$(\text{Ca,Sr})_{3}(\text{Ir,Rh})_{4}\text{Sn}_{13}$.Three of these cubic
compounds exhibit a microscopic coexistence of charge-density wave (CDW) order
and superconductivity (SC), while $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$
does not develop CDW order. As expected, the CDW transition temperature,
$T_{\text{CDW}}$, is universally suppressed by irradiation in all three
compositions. The superconducting transition temperature, $T_{c}$, behaves in a
more complex manner. In $\text{Sr}_{3}\text{Rh}_{4}\text{Sn}_{13}$, it
increases initially in a way consistent with a direct competition of CDW and
SC, but quickly saturates at higher irradiation doses. In the other three
compounds, $T_{c}$ is monotonically suppressed by irradiation. The strongest
suppression is found in $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$, which does
not have CDW order. We further examine this composition by measuring the London
penetration depth, $\lambda(T)$, from which we derive the superfluid density.
The result unambiguously points to a weak-coupling, full single gap, isotropic
superconducting state. Therefore, we must explain two seemingly incompatible
experimental observations: a single isotropic superconducting gap and a
significant suppression of $T_{c}$ by non-magnetic disorder. We conduct a
quantitative theoretical analysis based on a generalized Anderson theorem which
points to an unconventional multiband $s^{+-}$-pairing state where the sign of
the order parameter is different on one (or a small subset) of the smaller
Fermi surface sheets, but remains overall fully-gapped.
