  In a previous paper \cite{lp}, supersymmetric $p$-brane solutions involving
one dilatonic scalar field in maximal supergravity theories were classified.
Although these solutions involve a number of participating field strengths,
they are all equal and thus they carry equal electric or magnetic charges. In
this paper, we generalise all these solutions to multi-scalar solutions in
which the charges become independent free parameters. The mass per unit
$p$-volume is equal to the sum of these Page charges. We find that for generic
values of the Page charges, they preserve the same fraction of the
supersymmetry as in their single-scalar limits. However, for special values of
the Page charges, the supersymmetry can be enhanced.
