Generally speaking you cannot hold out for charter with a Part 125 cert. A typical exception would be if you were running a lets say a baseball team that owned and operated their own 757, they could with specific FAA approvals, charter that same airplane to another baseball, football or basketball team. There are limits on how this is structured regarding compensation etc.
Another example would the 757 that Trump owns. It is a classic example of a Part 125 operation.