The last time I was seriously looking at controlling a large number of LEDs I seem to recall seeing a number of multi-channel constant current drivers designed to be used with an external PWM signal, perhaps a setup like that would suit your needs? The trick then is providing a sufficient number of PWM outputs. If you only need 16 channels, you might be able to find a suitable micro with that many PWM outputs, or maybe an IO expander, or use the inverted output of the TLC5940, even. If you need more channels something like the LT8500 (48 channels, with some nice control features) might be a better fit.
If you can get away without the constant current drive, then of course you could simply use the TLC5940 to control an external transistor.
Thinking a little more out of the box, if you can arrange your circuit so that the TLC5940's Vcc is at +48V (with it's ground at +43V), then you could use a current mirror to turn its output current around and drive your LEDs from the high side. For higher currents that wouldn't be terribly efficient, though.