Recent legal changes have increased the need for developing accessible user interfaces in computer-based systems. In this sense, previously existing user interfaces are intended to be modified and new user interfaces are intended to be designed taking accessibility guidelines into account. Typically, model-based approaches have been used when developing accessible user interfaces or redefining existing ones. But the use of static models leads to the development of not dynamically adaptable user interfaces. Dynamic adaptation in accessible user interfaces is important due to the fact that interaction difficulties on people with disabilities may change through use. In this paper, we present some contributions that can be obtained from the application of the Dichotomic View of plasticity in the personalization of user interfaces. With the double perspective defined in this approach, it is intended to go further from a mere adaptation to certain user stereotypes, offering also a dynamic support to real limitations or difficulties users can encounter during the use of the UI. This goal is achieved analyzing user logs by an inference engine that dynamically infers modifications in the user interface to adjust it to varying user needs. A case study is presented in order to show how the guidelines and software support defined in the Dichotomic View of plasticity can be applied to develop a component for a particular system aimed at performing dynamic user interface adaptations with accessibility purposes. This approach includes some innovations that make it different from conventional adaptable mechanisms applied to accessibility in some important aspects.