verb, To arrange for
maximum benefit.
Finagling is a self-interested thing to do. It usually implies some sort of pseudo-underhandedness on the part of the parties doing the finagling. It also requires some level of expert knowledge of the system or relationship that is to be manipulated. As far as I know, this has nothing to do with Finagle's Law.
"So, you want to see 'moJoe's Madness', 'Pierceing Jessica', and 'pseudo_intellectual the Sway-Backed old Nag' to win, place and show in the third? I think I can finagle it for you; for the right price of course."