We present a scheme to enhance the atom number in magneto-optical traps of strontium atoms operating on the 461-nm transition. This scheme consists of resonantly driving the ${}^{1}{\mathrm{S}}_{0}\ensuremath{\rightarrow}{}^{3}{\mathrm{P}}_{1}$ intercombination line at 689 nm, which continuously populates a short-lived reservoir state and, as expected from a theoretical model, partially shields the atomic cloud from losses arising in the 461-nm cooling cycle. We show a factor of 2 enhancement in the atom number for the bosonic isotopes ${}^{88}\mathrm{Sr}$ and ${}^{84}\mathrm{Sr}$, and the fermionic isotope ${}^{87}\mathrm{Sr}$, in good agreement with our model. Our scheme can be applied in the majority of strontium experiments without increasing the experimental complexity of the apparatus, since the employed 689-nm transition is commonly used for further cooling. Our method should thus be beneficial to a broad range of quantum science and technology applications exploiting cold strontium atoms, and could be extended to other atomic species.