  In a sky-averaged 21-cm signal experiment, the uncertainty on the extracted
signal depends mainly on the covariance between the foreground and 21-cm signal
models. In this paper, we construct these models using the modes of variation
obtained from the Singular Value Decomposition of a set of simulated foreground
and 21-cm signals. We present a strategy to reduce this overlap between the
21-cm and foreground modes by simultaneously fitting the spectra from multiple
different antennas, which can be used in combination with the method of
utilizing the time dependence of foregrounds while fitting multiple drift scan
spectra. To demonstrate this idea, we consider two different foreground models
(i) a simple foreground model, where we assume a constant spectral index over
the sky, and (ii) a more realistic foreground model, with a spatial variation
of the spectral index. For the simple foreground model, with just a single
antenna design, we are able to extract the signal with good accuracy if we
simultaneously fit the data from multiple time slices. The 21-cm signal
extraction is further improved when we simultaneously fit the data from
different antennas as well. This improvement becomes more pronounced while
using the more realistic mock observations generated from the detailed
foreground model. We find that even if we fit multiple time slices, the
recovered signal is biased and inaccurate for a single antenna. However,
simultaneously fitting the data from different antennas reduces the bias and
the uncertainty by a factor of 2-3 on the extracted 21-cm signal.
