"weakened" operads

In their book "Homotopy invariant structures on topological structures", Boardman and Vogt construct from any topological operad O a new one WO, which can be thought of as a "weakened" version of O in which all the laws of O now hold only up to homotopy in a coherent way. Has there been any subsequent work clarifying this construction? Here I'm not interested so much in all the *other* approaches to infinite loop space machines, as in the notion of "weakening" a topological operad. For example, Boardman and Vogt point out that their construction can be used to discuss homotopy colimits, which makes me wonder if the construction of WO from O could be done slickly using homotopy colimits. Has anyone discussed this? Best, John Baez