  We study Kan extensions in three weakenings of the Eilenberg-Moore double
category associated to a double monad, that was introduced by Grandis and
Par\'e. To be precise, given a normal oplax double monad $T$ on a double
category $\mathcal K$, we consider the double categories consisting of pseudo
$T$-algebras, `weak' vertical $T$-morphisms, horizontal $T$-morphisms and
$T$-cells, where `weak' means either `lax', `colax' or `pseudo'. Denoting these
double categories by $\mathsf{Alg}_w T$, where w = l, c or ps accordingly, our
main result gives, in each of these cases, conditions ensuring that (pointwise)
Kan extensions can be lifted along the forgetful double functor $\mathsf{Alg}_w
T \to \mathcal K$. As an application we recover and generalise a result by
Getzler, on the lifting of pointwise left Kan extensions along symmetric
monoidal enriched functors. As an application of Getzler's result we prove, in
suitable symmetric monoidal categories, the existence of bicommutative Hopf
monoids that are freely generated by cocommutative comonoids.
