In the 1980s, Mahowald and Kane used Brown--Gitler spectra to construct splittings of $bo \wedge bo$ and $l \wedge l$. These splittings helped make it feasible to do computations using the $bo$- and $l$-based Adams spectral sequences. In this talk, we will discuss an analogous splitting for $BP\langle 2 \rangle \wedge BP \langle 2 \rangle$ at primes larger than $3$.