I think most DMMs will output less than 2mA, and you can't kill anything but MOSFET gates with such current.
2 milliamps is plenty to damage a bipolar transistor through base-emitter breakdown and it happens almost instantly. It permanently lowers the hfe increasing bias current and noise. This does not matter so much for RF transistors, switching transistors, and power transistors that operate with low hfe anyway but it ruins a differential input stage which is why operational amplifiers which lack a cascode input or wide differential input range (lateral PNP inputs) have input protection circuits limiting differential input voltage.
Various ohms meters that I have handy:
Tektronix DM501 10 Volts 1 Milliamp
Tektronix DM502 10 Volts 1 Milliamp
Tektronix DM501A 6 Volts 1 Milliamp
Beckman RMS225 0.6 Volts 0.8 Milliamps Ohms
Beckman RMS225 3.2 Volts 3.1 Milliamps Continuity
Tektronix DMM916 3.2 Volts 0.4 Milliamps Ohms and Continuity
Newer meters have a slightly higher test voltage so they can reliably test blue LEDs.