We show that dense OGLE and KMTNet I-band survey data require four bodies (sources plus lenses) to explain the microlensing light curve of OGLE-2015-BLG-1459. However, these can equally well consist of three lenses and one source (3L1S), two lenses and two sources (2L2S) or one lens and three sources (1L3S). In the 3L1S and 2L2S interpretations, the host is a brown dwarf and the dominant companion is a Neptune-class planet, with the third body (in the 3L1S case) being a Mars-class object that could have been a moon of the planet. In the 1L3S solution, the light curve anomalies are explained by a tight (five stellar radii) low-luminosity binary source that is offset from the principal source of the event by ∼0.17AU. These degeneracies are resolved in favor of the 1L3S solution by color effects derived from comparison to MOA data, which are taken in a slightly different (R/I) passband. We discuss implications for the observing strategies of current and future (WFIRST) observations that would enable them to distinguish among such exotic systems.