Complex learning tasks may be exhausting, tiring and sometimes even frustrating. Learners do need assistance. This is particularly true in technology enhanced learning where learners are frequently missing personalized guidance by some human teacher. The authors carefully distinguish adaptability, i.e. the possibility to adapt a system to varying needs and context conditions, from adaptivity, i.e. this system's ability to adapt its appearance and behavior to identified current needs autonomously. Among many others, the central necessity is to meet a learner's goal(s). High dimensional adaptivity is introduced, studied, implemented, and tried out towards better assistance to a large variety of learners under manifold circumstances in meeting the users' respective learning goals. The paper presents the concept of dimensions in adaptivity, illustrates the usefulness of the approach in an existing e-learning application, and explains several techniques in some more detail. Emphasis is put on novel opportunities enabled by innovative technologies. The DVDconnector technology, for instance, allows for the integration of large-size media like full-screen movies into online services. The content drawn from the DVD can be sashayingly dovetailed with online e-learning. DVD script programming makes even DVD content dynamic; it may be assembled and presented in dependence on learner needs. The aim of the paper is to provide a little contribution to the community's common endeavour to make our e-learning systems and services considerably more adaptive.