  We performed ab initio calculations in order to assess the reactivity of
ultracold RbSr ($^2\Sigma^+$) $+$ RbSr ($^2\Sigma^+$) collisions occurring on
the singlet as well as the triplet potential. At ultracold energies reactions
are energetically possible if they release energy, i.e., they are exoergic. The
exoergicity of reactions between RbSr molecules producing diatomic molecules
are known experimentally. We extend this to reactions producing triatomic
molecules by calculating the binding energy of the triatomic reaction products.
We find that, in addition to the formation of Rb$_2$+2Sr and Rb$_2$+Sr$_2$ in
singlet collisions, also the formation of Sr$_2$Rb+Rb and Rb$_2$Sr+Sr in both
singlet and triplet collisions is exoergic. Hence, the formation of these
reaction products is energetically possible in ultracold collisions. For all
exoergic reactions the exoergicity is larger than 1000 cm$^{-1}$. We also find
barrierless qualitative reaction paths leading to the formation of singlet
Rb$_2$+2Sr and both singlet and triplet Rb$_2$Sr+Sr and Sr$_2$Rb+Rb reaction
products and show that a reaction path with at most a submerged barrier exists
for the creation of the singlet Rb$_2$+Sr$_2$ reaction product. Because of the
existence of these reactions we expect ultracold RbSr collisions to result in
almost-universal loss even on the triplet potential. Our results can be
contrasted with collisions between alkali-diatoms, where the formation of
triatomic reaction products is endoergic, and with collisions between ultracold
SrF molecules, where during triplet collisions only the spin-forbidden
formation of singlet SrF$_2$ is exoergic.
