A new method to derive recurrence relations for the off-shell Bethe vectors in quantum integrable models with different symmetries will be discussed. These recurrence relations describe how to add new parameters to the specific subsets of the Bethe parameters, expressing the resulting Bethe vector as a linear combination of monodromy matrix entries acting on Bethe vectors which do not depend on added parameters. These results allow to investigate the scalar products of the Bethe vectors in the integrable models with general linear, orthogonal and symplectic symmetries.
