  The use of ultrathin solid foils offers optimal conditions for accelerating
protons from laser-matter interactions. When the target is thin enough that
relativistic self-induced transparency (RSIT) sets in, all of the target
electrons get heated to high energies by the laser, which maximizes the
accelerating electric field and therefore the final ion energy. In this work,
we first investigate how ion acceleration by ultraintense femtosecond laser
pulses in transparent CH$_2$ solid foils is modified when turning from normal
to oblique ($45^\circ$) incidence. Due to stronger electron heating, we find
that higher proton energies can be obtained at oblique incidence but in thinner
optimum targets. We then show that proton acceleration can be further improved
by splitting the laser pulse into two half-pulses focused at opposite incidence
angles. An increase by $\sim 30\,\%$ in the maximum proton energy and by a
factor of $\sim 4$ in the high-energy proton charge is reported compared to the
reference case of a single normally incident pulse.
