In most opamps, the slew rate is limited by the current that can be forced through Cdom by the input stage, but since most opamps use a long-tailed-pair input stage, that current is limited to double the quiescent current through the input devices.
To increase the slew rate with that kind of topology, you have to either reduce Cdom and/or increase the idling current, but there's obviously practical limits to how far you can go without running into other problems with e.g. quiescent power dissipation or input bias currents.
One neat way out of the trap is to start with an input stage whose maximum output current is
much higher than it's idling current. Essentially, you need a class AB input stage.
For example, the pic below shows a simplified schematic of the AD844, which boasts a slew rate of 2000V/uS. It's a little unusual in another respect as well, since it's better suited to current feedback than voltage feedback. As the datasheet explains.....