  We consider Lipschitz maps with values in quasi-metric spaces and extend such
maps to finitely many points. We prove that in this context every 1-Lipschitz
map admits an extension such that its Lipschitz constant is bounded from above
by the number of added points plus one. Moreover, we prove that if the source
space is a Hilbert space and the target space is a Banach space, then there
exists an extension such that its Lipschitz constant is bounded from above by
the square root of the total of added points plus one. We discuss applications
to metric transforms.
