If you are duplicating the whole circuit 24 times, there will be no problem. But I guess you are just adding 23 more relays in parallel, right?
You need to figure out if the relay is on or off; if on, ignore additional triggers. If off, wait for the trigger pulse.
If not critical, think of introducing random delays between the relay turn-on:s. That will be just showing some kindness on the power supply.
I guess all the 24 relays are being turned on simultaneously with one common trigger?