CPRman, first thing I would ask is where did you pull your scores? If not from myFICO, they are probably not true FICO scores.
Getting a new CC willl almost certainly NOT inprove your current FICO, in the short term.
A new CC will hit you for a hard inq It will also shorten your avg age of accounts. The only short term benefit is an increase in CL. If the new CC is to build account age years from now, that is a long term consideration that is a possible future benefit, but a deficit now.
The most recent data presented by FairIsaac before the FTC shows that their risk analysis of the number of open CCs is that 3-4 is optimal, and that above that, the risk rises.