Call a model structure on $Top$ (the category of topological spaces) standard, if the weak equivalences are the weak homotopy equivalences. In this nLab page, two standard model structures on $Top$ are defined. One is the Quillen model structure, in which fibrations are the Serre fibrations, and one is the Mixed model structure, in which the fibrations are the Hurewicz fibrations. Since every Hurewicz fibrations is a Serre fibration, The Mixed Model Structure has more cofibrations then the Quillen Model Structure. For e.g., the cofibrant objects in the Mixed model structure are the topological spaces that are homotopy equivalent to $CW$-complexs, while the cofibrant objects in the Quillen model structure are the topological spaces that are retracts of $CW$-complexs. My Question is the following:

Is there a standard model structure on $Top$ with more cofibrations then the Mixed model structure?