We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfeld double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi--Lie bialgebra, extending the known correspondence between a Lie bialgebra and a Drinfeld double. We then construct generalized frame fields $E_A{}^Mintext{O}(D,D)timesmathbb{R}^+$ satisfying the algebra $mathcal{L}_{E_A}E_B = - X_{AB}{}^C,E_C,$, where $X_{AB}{}^C$ are the structure constants of the DD$^+$ and $mathcal{L}$ is the generalized Lie derivative in double field theory. Using the generalized frame fields, we propose the Jacobi-Lie T-plurality and show that it is a symmetry of double field theory. We present several examples of the Jacobi-Lie T-plurality with or without Ramond-Ramond fields and the spectator fields.
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