Non-uniqueness of certain Hahn - Banach extensions

Let f be a continuous linear functional defined on a subspace M of a normed space X. If X is real or complex, there are results that characterize uniqueness of continuous extensions F of f to X for every subspace M and those that apply just to M. If X is defined over a non-Archimedean valued field K and the norm also satisfies the strong triangle inequality, the Hahn--Banach theorem holds for all subspaces M of X if and only if K is spherically complete and it is well-known that Hahn--Banach extensions are never unique in this context. We give a different proof of non-uniqueness here that is interesting for its own sake and may point a direction in which further investigation would be fruitful.