A bi-weekly challenge from Andre Mirabelli & Opturo

When using a Dietz calculation for the returns of traded components of a portfolio on a single day, do all components have to use the same timing rule, or can some use all trades at open and others use purchases at open and sales at the close, etc., and still have these component returns roll up to the correct portfolio return?
And how should the “cash” bucket, into which sale proceeds are put or from which purchases are funded, get treated in all these cases?