1)Let $X$ be a differentiable stack ((2,1) sheaf over the category of smooth manifolds $Man$) and that is geometric. Let $N\in Man$, then $$ Map(y(N),X) $$ is again a differentiable stack ($y$ is the Yoneda embedding). Assume that $X$ is represented by the Lie groupoid $(M_{0}, M_{1}, s,t)$. How to find a "good" Lie groupoid that represents $Map(y(N),X)$ (i.e., something that depend by $N, M_{0}, M_{1}, s$ and $t$)?
2) Assume that $X$ is a sheaves of simplicial sets over $Man$. If $X$ is $n$-geometric, then so is $Map(y(N),X)$. How to find a $n$-Lie groupoid that represents $Map(y(N),X)$?
Edit: As Dimitri Pavlov pointed out, it is not clear what does it means representability here. I'm looking for a simplicial possibly $\infty$ dimensional manifold (or simplicial diffeological space) $Z_{\bullet}$ such that
a) $y(Z_{\bullet})$ is a simplicial presheaf
b) the stackification of $y(Z_{\bullet})$ is weak equivalent to $Map(y(N),X)$
(hence for the case 1) I looking for a 2-truncated simplicial possibly $\infty$ dimensional manifold (or simplicial diffeological space) $Z_{\bullet}$, that enjoys the above properties.)