The eXtended Continuum Discretized Coupled Channel (XCDCC) method is developed to treat reactions where core degrees of freedom play a role. The projectile is treated as a multi-configuration coupled channels system generated from a valence particle coupled to a deformed core which is allowed to excite. The coupled channels initial state breaks up into a coupled channels continuum which is discretized into bins, similarly to the original CDCC method. Core collective degrees of freedom are also included in the interaction of the core and the target, so that dynamical effects can occur during the reaction. We present results for the breakup of $^{17}$C=$^{16}$C+n and $^{11}$Be=$^{10}$Be+n on $^{9}$Be. Results show that the total cross section increases with core deformation. More importantly, the relative percentage of the various components of the initial state are modified during the reaction process through dynamical effects. This implies that comparing spectroscopic factors from structure calculations with experimental cross sections requires more detailed reaction models that go beyond the single particle model.
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