We present detailed multi-frequency , multi-epoch radio observations of GRB 140304A at z = 5.283 from 1 to 86 GHz and 0.45 d to 89 d. The radio and mm data exhibit unusual multiple spectral components , which can not be simply explained by standard forward and reverse shock scenarios . Through detailed multi-wavelength analysis spanning radio to X-rays , we constrain the forward shock parameters to E _ { K,iso } \approx 4.9 \times 10 ^ { 54 } erg , A _ { * } \approx 2.6 \times 10 ^ { -2 } , \epsilon _ { e } \approx 2.5 \times 10 ^ { -2 } , \epsilon _ { B } \approx 5.9 \times 10 ^ { -2 } , p \approx 2.6 , and \theta _ { jet } \approx 1.1 ^ { \circ } , yielding a beaming corrected \gamma -ray and kinetic energy , E _ { \gamma } \approx 2.3 \times 10 ^ { 49 } erg and E _ { K } \approx 9.5 \times 10 ^ { 50 } erg , respectively . We model the excess radio emission as due to a combination of a late-time reverse shock ( RS ) launched by a shell collision , which also produces a re-brightening in the X-rays at \approx 0.26 d , and either a standard RS or diffractive interstellar scintillation . Under the standard RS interpretation , we invoke consistency arguments between the forward and reverse shocks to derive a deceleration time , t _ { dec } \approx 100 s , the ejecta Lorentz factor , \Gamma ( t _ { dec } ) \approx 300 , and a low RS magnetization , R _ { B } \approx 0.6 . Our observations highlight both the power of radio observations in capturing RS emission and thus constraining the properties of GRB ejecta and central engines , and the challenge presented by interstellar scintillation in conclusively identifying RS emission in GRB radio afterglows .