  We consider extension of a closure system on a finite set S as a closure
system on the same set S containing the given one as a sublattice. A closure
system can be represented in different ways, e.g. by an implicational base or
by the set of its meet-irreducible elements. When a closure system is described
by an implicational base, we provide a characterization of the implicational
base for the largest extension. We also show that the largest extension can be
handled by a small modification of the implicational base of the input closure
system. This answers a question asked in [12]. Second, we are interested in
computing the largest extension when the closure system is given by the set of
all its meet-irreducible elements. We give an incremental polynomial time
algorithm to compute the largest extension of a closure system, and left open
if the number of meet-irreducible elements grows exponentially.
