The extremely inflated sub-Saturn KELT-11b has one of the lowest surface gravities of any planet discovered to date. It also has a high equilibrium temperature and a host star that is a bright, metal-rich, sub-giant that is part of the retired A-star class. This makes KELT-11b one of the best and most interesting targets for atmospheric characterization. Here, we present an optical-to-infrared transmission spectrum of KELT-11b measured with the Transiting Exoplanet Survey Satellite (TESS), the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) G141 spectroscopic grism, and the Spitzer Space Telescope (Spitzer) at 3.6 um, in addition to a Spitzer 4.5 um secondary eclipse. The TESS observations cover five full transits of KELT-11b and particularly provide the only precise optical transit depth for this planet so far, outside of the single transit of KELT-11b observed recently with CHEOPS. Furthermore, the precise near-infrared HST transmission spectrum notably reveals a low-amplitude water feature with an unusual shape. We performed a number of free retrieval analyses and find strong evidence for water absorption in the spectrum and tentative evidence for other absorbers, depending on model assumptions. In particular, the higher transit depth of the TESS data point relative to the HST data is preferentially explained by some additional optical absorber like Na, K, TiO, or AlO. The retrieved water abundance is generally less than 0.1x solar, which is several orders of magnitude lower than expected from planet formation models based on the solar system metallicity trend. We also consider chemical equilibrium and self-consistent 1D radiative-convective equilibrium model fits and find that they too prefer low metallicities ([M/H] less than -2, consistent with the free retrieval results). Finally, we find that the dayside flux measured from the Spitzer secondary eclipse is indicative of full heat redistribution from KELT-11b’s dayside to nightside, assuming the a clear dayside. Altogether, these potentially unusual results for KELT-11b’s composition derived from TESS, HST, and Spitzer observations are suggestive of new challenges on the horizon for atmosphere and formation models in the face of increasingly precise measurements of exoplanet spectra. We also describe additional observations of KELT-11b that we anticipate will help solve the atmospheric puzzle of this intriguing exoplanet.