If $r≥4$ then can the sum of $r-2$ coprime $r$-powerful numbers ever be itself $r$-powerful?

Euler had conjectured that the sum of $k - 1$ many $k$-th powers is never a $k$-th power, but this is false for $k=5$, as Lander and Parkin [LaPa67] found $$27^5+84^5+110^5+133^5=144^5$$.

[LaPa67] Lander, L. J. and Parkin, T. R., "A counterexample to Euler's sum of powers conjecture." Math. Comp. (1967), 101--103.