It's hard with a regular multimeter but it would be possible to get a reasonably close measurement of the current using a clampmeter (which can also work as a regular multimeter, but for the price you'd pay for a clampmeter you would get a more specialized multimeter, so think of the regular multimeter part as a bonus.
You would need a multimeter that can also measure DC current. A cheap and more than good enough clampmeter would be Uni-T UT210 :
https://amzn.to/2ISWmCESo basically what you would do is start the clampmeter in DC current mode, then insert the +24v wire(s) between the psu and the board (or whatever) in the center of your clamp, and the meter will tell you the amount of current going through the wire. The measurement will vary slightly with the position of the wire inside the clamp, so it's best to be consistent if you make multiple measurements and keep the wire(s) as close as possible to the center.
If the current flowing through the wire is too small, you can practically make a loop through the clamp, for every loop the meter will show double the actual current value or something like that.
That's pretty much it... you just have to separate the positive and negative wires and only insert one type through the clamp otherwise you won't get a good measurement.