Multiple superconducting transitions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Yb</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi

In the Yb-Co-Sn system a Remeika phase ${\mathrm{Yb}}_{3+x}{\mathrm{Co}}_{4}{\mathrm{Sn}}_{13\ensuremath{-}x}$ is found with solid solution extending within $0\ensuremath{\le}x\ensuremath{\le}0.5$. All these compounds crystallize with primitive cubic (space group $Pm\overline{3}n, a\ensuremath{\approx}9.54\phantom{\rule{0.16em}{0ex}}\AA{}$) strongly disordered ${\mathrm{Sc}}_{3}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{13+x}$ type. Stoichiometric ${\mathrm{Yb}}_{3}{\mathrm{Co}}_{4}{\mathrm{Sn}}_{13}$ is a superconductor with critical temperature ${T}_{c}=3.1(2)\phantom{\rule{4pt}{0ex}}\mathrm{K}$, lower- $[{B}_{\mathrm{c}}1=1.90(2)\phantom{\rule{0.16em}{0ex}}\mathrm{mT}]$ and upper $[{B}_{\mathrm{c}}2=2.16(5)\phantom{\rule{0.16em}{0ex}}\mathrm{T}]$ critical fields. The specific-heat jump $\mathrm{\ensuremath{\Delta}}{c}_{p}/\ensuremath{\gamma}{T}_{c}=1.72(9)$ together with the fact that ${B}_{\mathrm{c}}2({T}_{c})$ dependence is described by the Werthamer-Helfand-Hohenberg (WHH) model hint toward a conventional mechanism with a weak electron-phonon coupling. Although a more precise analysis is hampered by the presence of multiple superconducting transitions observed in the specific heat of this Remeika phase, the nonstoichiometric ${\mathrm{Yb}}_{3.2}{\mathrm{Co}}_{4}{\mathrm{Sn}}_{12.8}$ reveals ${T}_{c}=2.4(2)\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and ${B}_{\mathrm{c}}2=4.79(9)\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ exceeding the classical Pauli limit. Strong electron-phonon coupling in this superconductor is confirmed by the high value of the ${\ensuremath{\lambda}}_{\mathrm{AD}}=0.92(2)$ parameter determined from the Allen-Dynes formula. However, the electronic specific heat of ${\mathrm{Yb}}_{3.2}{\mathrm{Co}}_{4}{\mathrm{Sn}}_{12.8}$ follows the exponential law $[{c}_{\mathrm{el}}(T)\ensuremath{\propto}{e}^{\ensuremath{-}\mathrm{\ensuremath{\Delta}}(0)/{k}_{\mathrm{B}}T}]$ and can be described by the $\ensuremath{\alpha}$-model $[\ensuremath{\alpha}\ensuremath{\equiv}\mathrm{\ensuremath{\Delta}}(0)/{k}_{\mathrm{B}}{T}_{c}=2]$ indicating this stannide to be a conventional BCS-superconductor. Both ${\mathrm{Yb}}_{3+x}{\mathrm{Co}}_{4}{\mathrm{Sn}}_{13\ensuremath{-}x}$ ($x=0,0.2$) compounds reveal complex phonon spectra with possible ``rattling'' behavior. They are also found to be metallic systems, some aspects of which can be described by a free-electron-gas model.