Summary: A family of algebras \(\mathcal{E}_n\) that extends the Lie algebra of the Drinfel’d double is proposed. This allows us to systematically construct the generalized frame fields \(E_A^I\) which realize the proposed algebra by means of the generalized Lie derivative, i.e., \(\hat{\mathcal L}_{E_A}E_B{}^I=-\mathcal{F}_{AB}{}^C E_C{}^I\). By construction, the generalized frame fields include a twist by a Nambu-Poisson tensor. A possible application to the non-abelian extension of \(U\)-duality and a generalization of the Yang-Baxter deformation are also discussed.