  We investigate the effect of extending the standard MSTW parameterisation of
input parton distribution functions (PDFs) using Chebyshev polynomials. We find
evidence that four powers in the polynomial are sufficient for extremely high
precision. Applying this to valence and sea quarks we find an improvement in
the global fit, but a significant change only in the small-$x$ valence up-quark
PDF, $u_V$. We investigate the effect of also extending, and making more
flexible, the `nuclear' correction to deuteron structure functions. The
extended `Chebyshev' parameterisation results in an improved stability in the
deuteron corrections that are required for the best fit to the `global' data.
The resulting PDFs have a significantly, but not dramatically, altered valence
down-quark distribution, $d_V$. For the extended set of MSTW PDFs, their
uncertainties can be obtained using 23, rather than the usual 20, orthogonal
`uncertainty' eigenvectors. Since the dominant effect is on the valence quarks,
we present a detailed study of the dependence of the valence--sea separation on
the predictions for the decay lepton charge asymmetry which results from
$W^\pm$ production at the LHC, illustrating the PDFs and the $x$ range probed
for different experimental scenarios. We show that the modified MSTW PDFs make
significantly improved predictions for these data at the LHC, particularly for
high values of the $p_T$ cut of the decay lepton. However, this is a special
case, since the asymmetry is extremely sensitive to valence--sea details, and
in particular to the combination $u_V-d_V$ of valence PDFs for $x \sim
M_W/\sqrt{s}$ at low lepton rapidities. We show that the predictions for a wide
variety of total cross sections are very similar to those obtained using the
MSTW2008 PDFs, with changes being much smaller than the PDF uncertainties.
