  We consider the extensions of classical r-matrix for \kappa-deformed
Poincar\'{e} algebra which satisfy modified Yang-Baxter equation. Two examples
introducing additional deformation parameter (dimensionfull
\frac{1}{\widetilde{\kappa}} or dimensionless \xi) are presented. We describe
the corresponding quantization (two-parameter \kappa-Poincar\'{e} quantum Hopf
algebras) in explicite form as obtained by twisting of standard \kappa-deformed
framework. In the second example quantum twist function depends on nonclassical
generators, with \kappa-deformed coproduct. Finally we mention also the
``soft'' twists with carrier in fourmomenta sector.
