Classification of special Hopf algebras

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Is there a classifications of (connected+ finite-dimensional) algebras A that are Hopf algebras with indecomposable projective modules $P_1,...,P_n$, such that every algebra of the form $B=End_A( P_1^{m_1} \oplus ... \oplus P_n^{m_n})$ (which is morita equivalent to A) is also a Hopf algebra as long as one $m_i=1$?