  This paper deals with scalar linear index codes for canonical multiple
unicast index coding problems where there is a source with K messages and there
are K receivers each wanting a unique message and having symmetric (with
respect to the receiver index) antidotes (side information). Optimal scalar
linear index codes for several such instances of this class of problems have
been reported in \cite{MRRarXiv}. These codes can be viewed as special cases of
the symmetric unicast index coding problems discussed in \cite{MCJ}. In this
paper a lifting construction is given which constructs a sequence of multiple
unicast index problems starting from a given multiple unicast index coding
problem. Also, it is shown that if an optimal scalar linear index code is known
for the problem given starting problem then optimal scalar linear index codes
can be obtained from the known code for all the problems arising from the
proposed lifting construction. For several of the known classes of multiple
unicast problems our construction is used to obtain several sequences of
multiple unicast problem with optimal scalar linear index codes.
