  We present the explicit construction of some multi-scalar field theories in
(1+1) dimensions supporting BPS (Bogomol'nyi--Prasad--Sommerfield) kink
solutions. The construction is based on the ideas of the so-called extension
method. In particular, several new interesting two-scalar and three-scalar
field theories are explicitly constructed from non-trivial couplings between
well-known one-scalar field theories. The BPS solutions of the original
one-field systems will be also BPS solutions of the multi-scalar system by
construction, and therefore we will analyse their linear stability properties
for the constructed models.
