Working in ZfC + Wholeness:

Can we have a countable sequence of non-trivial elementary embeddings of the universe to itself, such that the range of each embedding is a subclass of the range of its successor, and such that the union of all the ranges of those embeddings is the universe itself?

Formally can we have a proper class sequence $j`\mathbb N$ such that:

$\forall n \in \mathbb N : j_n: V \prec V \land rng(j_{n+1}) \supset rng(j_n) \\ \forall x \exists n \in \mathbb N : x \in rng(j_n)$

Where $\mathbb N$ is the set of all finite von Neumann ordinals.

Note: ZfC means ZFC but with replacement restricted to the pure language of set theory, i.e. it doesn't use the symbol $j$; however, $j$ is allowed in all instances of separation.