Frames can be seen as generalized bases, that is, over-complete collections, which are used for stable representations of signals as linear combinations of basic building atoms. It is very useful when we can use locally adapted atoms, which in addition behave as elements of local bases. We explore the possibility of using localized parts of frames and bases when building a customized frame. After a review on Gabor frames and Wilson bases, we consider the question of combining parts of these collections into a multi-frame set and look at its properties.