  Amalgamation is investigated in classes of non-divisible, non-in\-teg\-ral,
and non-idempotent involutive commutative residuated lattices. We demonstrate
that several subclasses of totally-ordered, involutive, commutative residuated
lattices fail the Amalgamation Property. These include the classes of odd and
even ones, sharing the same underlying reason for their failure as observed in
the class of discrete linearly ordered abelian groups with positive normal
homomorphisms. Conversely, it is proven that three subclasses formed by
idempotent-symmetric, totally-ordered, involutive, commutative residuated
lattices possess the Amalgamation Property, albeit fail the Strong Amalgamation
Property. This failure shares the same underlying reason as observed in the
class of linearly ordered abelian groups. Additionally, it is demonstrated that
the varieties of semilinear, idempotent-symmetric, odd, involutive, commutative
residuated lattices and semilinear, idempotent-symmetric, odd or even,
involutive, commutative residuated lattices have the Transferable Injections
Property. Finally, it is shown that any variety of semilinear involutive
commutative residuated lattices that includes the variety of odd semilinear
commutative residuated lattices fails the Amalgamation Property.
