  The planetary infrared excess (PIE) technique has the potential to
efficiently detect and characterize the thermal spectra of both transiting and
non-transiting exoplanets. However, the technique has not been evaluated on
multiplanet systems. We use the TRAPPIST-1 system as our test bed to evaluate
PIE's ability to resolve multiple planets. We follow the unfolding discoveries
in the TRAPPIST-1 system and examine the results from the PIE technique at
every stage. We test the information gained from observations with JWST and
next-generation infrared observatories like the proposed MIRECLE mission
concept. We find that even in the case where only the star is known, the PIE
technique would infer the presence of multiple planets in the system. The
precise number inferred is dependent on the wavelength range of the observation
and the noise level of the data. We also find that in such a tightly packed,
multiplanet system such as TRAPPIST-1, the PIE technique struggles to constrain
the semi-major axis beyond prior knowledge. Despite these drawbacks and the
fact that JWST is less sensitive to the fluxes from planets g and h, with
strong priors in their orbital parameters we are able to constrain their
equilibrium temperatures. We conclude that the PIE technique may enable the
discovery of unknown exoplanets around solar-neighborhood M dwarfs and could
characterize known planets around them.
