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We perform an effective field theory analysis to correlate the charged lepton flavor violating processes ${\ensuremath{\ell}}_{i}\ensuremath{\rightarrow}{\ensuremath{\ell}}_{j}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${\ensuremath{\ell}}_{i}\ensuremath{\rightarrow}{\ensuremath{\ell}}_{j}\ensuremath{\gamma}$. Using current upper bounds on rate for ${\ensuremath{\ell}}_{i}\ensuremath{\rightarrow}{\ensuremath{\ell}}_{j}\ensuremath{\gamma}$, we derive model-independent limits rates ${\ensuremath{\ell}}_{i}\ensuremath{\rightarrow}{\ensuremath{\ell}}_{j}\ensuremath{\gamma}\ensuremath{\gamma}$. Our indirect are about three orders of magnitude stronger than direct from searches $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}\ensuremath{\gamma}$, four better $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\ell}\ensuremath{\gamma}\ensuremath{\gamma}$. also stress relevance Belle II or a Super Tau Charm Facility discover rare decay