  A rooted digraph is a vertex-flame if for every vertex $v$ there is a set of
internally disjoint directed paths from the root to $v$ whose set of terminal
edges covers all ingoing edges of $v$. It was shown by Lov\'{a}sz that every
finite rooted digraph admits a spanning subdigraph which is a vertex-flame and
large, where the latter means that it preserves the local connectivity to each
vertex from the root. A structural generalisation of vertex-flames and
largeness to infinite digraphs was given by the third author and the analogue
of Lov\'{a}sz' result for countable digraphs was shown. We strengthen this
result by proving that in every countable rooted digraph each vertex-flame can
be extended to a large vertex-flame.
