  We present a method to construct conformally curved initial data for charged
black hole binaries with spin on arbitrary orbits. We generalize the superposed
Kerr-Schild, extended conformal thin sandwich construction from [Lovelace et
al., Phys. Rev. D {78}, 084017 (2008)] to use Kerr-Newman metrics for the
superposed black holes and to solve the electromagnetic constraint equations.
We implement the construction in the pseudospectral code SGRID. The code thus
provides a complementary and completely independent excision-based
construction, compared to the existing charged black hole initial data
constructed using the puncture method [Bozzola and Paschalidis, Phys. Rev. D
{99}, 104044 (2019)]. It also provides an independent implementation (with some
small changes) of the Lovelace et al. vacuum construction. We construct initial
data for different configurations of orbiting binaries, e.g., with black holes
that are highly charged or rapidly spinning (90 and 80 percent of the extremal
values, respectively, for this initial test, though the code should be able to
produce data with even higher values of these parameters using higher
resolutions), as well as for generic spinning, charged black holes. We carry
out exploratory evolutions with the finite difference, moving punctures codes
BAM (in the vacuum case) and HAD (for head-on collisions including charge),
filling inside the excision surfaces. In the charged case, evolutions of these
initial data provide a proxy for binary black hole waveforms in modified
theories of gravity. Moreover, the generalization of the construction to
Einstein-Maxwell-dilaton theory should be straightforward.
