Living tissues show an extraordinary adaptiveness to strain, which is crucial for their proper biological functioning 1,2. The physical origin of this mechanical behaviour has been widely investigated using reconstituted networks of collagen fibres, the principal load-bearing component of tissues 3–5. However, collagen fibres in tissues are embedded in a soft hydrated polysaccharide matrix, which generates substantial internal stresses, and the effect of this on tissue mechanics is unknown 6–8 . Here, by combining mechanical measurements and computer simulations, we show that networks composed of collagen fibres and a hyaluronan matrix exhibit synergistic mechanics characterized by an enhanced stiffness and delayed strain stiffening. We demonstrate that the polysaccharide matrix has a dual effect on the composite response involving both internal stress and elastic reinforcement. Our findings elucidate how tissues can tune their strain-sensitivity over a wide range and provide a novel design principle for synthetic materials with programmable mechanical properties.