  The large-scale structure of the Universe should soon be measured at high
redshift during the Epoch of Reionization (EoR) through line-intensity mapping.
A number of ongoing and planned surveys are using the 21 cm line to trace
neutral hydrogen fluctuations in the intergalactic medium (IGM) during the EoR.
These may be fruitfully combined with separate efforts to measure large-scale
emission fluctuations from galactic lines such as [CII], CO, H-$\alpha$, and
Ly-$\alpha$ during the same epoch. The large scale power spectrum of each line
encodes important information about reionization, with the 21 cm power spectrum
providing a relatively direct tracer of the ionization history. Here we show
that the large scale 21 cm power spectrum can be extracted using only
cross-power spectra between the 21 cm fluctuations and each of two separate
line-intensity mapping data cubes. This technique is more robust to residual
foregrounds than the usual 21 cm auto-power spectrum measurements and so can
help in verifying auto-spectrum detections. We characterize the accuracy of
this method using numerical simulations and find that the large-scale 21 cm
power spectrum can be inferred to an accuracy of within 5% for most of the EoR,
reaching 0.6% accuracy on a scale of $k\sim0.1\,\text{Mpc}^{-1}$ at $\left< x_i
\right> = 0.36$ ($z = 8.34$ in our model). An extension from two to $N$
additional lines would provide $N(N-1)/2$ cross-checks on the large-scale 21 cm
power spectrum. This work strongly motivates redundant line-intensity mapping
surveys probing the same cosmological volumes.

Cosmology and Nongalactic Astrophysics