The board might be able to handle three fans on one header, but it depends on the fans being used.
The usual specs for fan headers currently is one Amp or 12 Watts each. I did read in this forum that supposedly ASRock Tech support said the Chassis fan headers on at least some boards were limited to 0.5 Amp or 6 Watts. I don't know if that is true or not.
Check the specs for the fans you have, which will most likely show the maximum current/Amp rating. That is usually printed on the fans label. You can either add up the Amp ratings of your fans, or multiply the Amp spec by 12 (for 12V) to get the power in Watts.
For example, if the fan's current/Amp spec is 0.20A, then the power it uses is: 12V X 0.20A = 2.4 Watts. Three of those fans would be 7.2 Watts max, so would be fine.
What fans will you be using?