The use of artificial defects is known to enhance the superconducting critical parameters of thin films. In the case of conventional superconductors, regular arrays of submicron holes (antidots) substantially increase the critical temperature T-c(H) and critical current I-c(H) for all fields. Using electrical transport measurements, we study the effect of placing an additional small antidot in the unit cell of the array. This composite antidot lattice consists of two interpenetrating antidot square arrays with a different antidot size and the same lattice period. The smaller antidots are located at the centers of the cells of the large antidots array. We show that the composite antidot lattice can trap a higher number of flux quanta per unit cell inside the antidots compared to a reference antidot film without the additional small antidots. As a consequence, the field range in which an enhanced critical current is observed is considerably expanded. Finally, the possible stable vortex lattice patterns at several matching fields are determined by molecular-dynamics simulations.