  We consider TASEP with two types of particles starting at every second site.
Particles to the left of the origin have jump rate $1$, while particles to the
right have jump rate $\alpha$. When $\alpha<1$ there is a formation of a shock
where the density jumps to $(1-\alpha)/2$. For $\alpha<1$ fixed, the statistics
of the associated height functions around the shock is asymptotically (as time
$t\to\infty$) a maximum of two independent random variables as shown
in\cite{FN14}. In this paper we consider the critical scaling when $1-\alpha=a
t^{-1/3}$, where $t\gg 1$ is the observation time. In that case the decoupling
does not occur anymore. We determine the limiting distributions of the shock
and numerically study its convergence as a function of $a$. We see that the
convergence to $F_{\rm GOE}^2$ occurs quite rapidly as $a$ increases. The
critical scaling is analogue to the one used in the last passage percolation to
obtain the BBP transition processes\cite{BBP06}.
