The spontaneous muonium to antimuonium conversion is one of the interesting
charged lepton flavor violation processes. It serves as a clear indication of
new physics and plays an important role in constraining the parameter space
beyond Standard Model. MACE is a proposed experiment to probe such a phenomenon
and expected to enhance the sensitivity to the conversion probability by more
than two orders of magnitude compared with the current best upper constraint obtained by the PSI experiment two decades ago. Recent progress in the conceptual design study will be reported, focusing on the beamline requirements, the high-efficency muonium formation in the target, an optimized design of magnetic spectrometer, the tracking algorithm to discriminate signals and backgrounds.