This paper presents a novel, parameteric framework for synthesizing new character motions from existing motion capture data. Our framework can conduct morphological adaptation as well as kinematic and physically-based corrections. All these solvers are organized in layers in order to be easily combined together. Given locomotion as an example, the system automatically adapts the motion data to the size of the synthetic figure and to its environment; the character will correctly step over complex ground shapes and counteract with external forces applied to the body. Our framework is based on a frame-based solver. This ensures animating hundreds of humanoids with different morphologies in real-time. It is particularly suitable for interactive applications such as video games and virtual reality where a user interacts in an unpredictable way.