(1) Timb gave you the most important piece of information you need to understand what can and CANNOT be achieved here:
Think about Ohm's Law.
This will
always be true. Plug in any two parameters and the third will be immediately determined. There is no room for discussion on this. It is simple arithmetic that cannot be 'got around'.
(2) The next most important thing is to realise that you are taking the term 'constant current' far too literally - and you are
completely ignoring the limiting conditions. You would be far better off thinking of such a supply as a
current limiting one.
(3) The regulation capability of any power supply has limits (upper and lower ... but we will just look at the maximums for this discussion). There is a maximum voltage that it can deliver and there is a maximum current it can deliver. Any values in excess of these indicate an area of operation that the supply simply cannot achieve - and any attempt to implement these values will result in the supply falling out of (the desired) regulation.
With these three things in mind, we can look at a couple of examples...
Let's say we want to push a constant 1A through a load - which is, say, 10 ohms. (I will stick to simple resistive loads for this part of the discussion.) Using Ohm's Law, we need the terminal voltage to be 10V. This is great - your supply can do this without any worries. Set the voltage to 10V and have the current control turned up to the maximum so it doesn't interfere. The actual current that flows will be a function of the voltage and load according to Ohm's Law.
Now, let's set the voltage to 20V.
Using the same load of 10 ohms, you are going to get 2A flowing - simple Ohm's Law (again)! To get the current we want, we are now going to have to wind back the current adjustment control until we get only 1A flowing. So , now that we've done that - what voltage is coming out of the supply? 20V you say? Wrong. It's actually 10V - it cannot be anything else.
What has happened is that the supply has altered the voltage it delivers to make sure the current limit is not exceeded. If you change the load to 5 ohms or 15 ohms or 18.65 ohms, the supply will limit the current to 1A by changing the voltage. This is how a constant current source works.
Now, what happens if we have a load of 50 ohms and we still want that 1A to flow?
Ohm's Law shows us that the supply needs to deliver 50V. That is a problem for a supply that can only go up to 20V. So what happens? It's really very simple - and Ohm's Law gives the answer (yet again).
Your supply puts out 20V and the 50 ohm load will draw 400mA.
That's it.
The current limit setting doesn't come into play, because the current is not trying to exceed that limit.
In theory, a truly 'constant current' source must have the capability to deliver an infinite voltage ... which is kinda difficult.