Sums of toric ideals

Given two toric ideals $I_1,I_2\subset \text{si}$, it is not always true that $I_1+I_2$ is a toric ideal. Given $I_1,\mathrm{.}\mathrm{.}\mathrm{.},I_k\subset \text{si}$ a familly of toric ideals we give necessary conditions in order to have that $I_1+\mathrm{.}\mathrm{.}\mathrm{.}+I_k$ is a toric ideal.