I've done some work on engine rating developments. In the engine ratings, Max Climb can never be higher than CON - CON occurs at a higher throttle position than max climb and it's a big no-no to the regulations to have thrust drop with increased throttle angle.
Now, there may be cases with a big derate takeoff where the usable CON rating is less than the Max Climb rating, but that'll be due to aircraft handling considerations (e.g. what the FMC displays). For example, it's well known that the 737 has a significant pitch-up characteristic with increasing thrust. In an extreme case, with a lightweight aircraft selecting max rated (CON or TO) thrust at low airspeed could result a greater pitch-up moment than can readily be controlled via the tail. But it you push the throttle to the firewall, you'll get either Max Con or Max Takeoff thrust (depending on the altitude/airspeed).
At least on the aircraft I worked (747-400, 767), Max CON and Max Climb were the same over 30k. So above 30k, there would just be a big 'flat' above the Max Climb TRA.