Perhaps now is the time for you to tell us what you are trying to do. You keep talking about a constant current source, but don't want it to change the output voltage, which is an oxymoron. Tell us what you want to accomplish, in terms of the voltage, current, and load.
Perhaps this will help. You have 3 variables, voltage, current, and load (resistance). Do you understand that if you cannot specify all 3 of them at the same time? If you specify any 2, the other 1 is determined.
Bob