  For type II supergravity backgrounds with superisometries the corresponding
transformations and conserved currents for the superstring are constructed up
to fourth order in $\Theta$. It is then shown how, for certain backgrounds
related to near horizon geometries of intersecting branes, the components of
the superisometry current can be used to construct a Lax connection
demonstrating the classical integrability of the string in these backgrounds.
This includes examples of $AdS_2$ and $AdS_3$ backgrounds with a
$D(2,1;\alpha)$ isometry group which have not previously been studied from an
integrability point of view. The construction of the Lax connection is carried
out up to second order in $\Theta$.
