I think It's allowed to send more than 2 PM's in one day but limited to 5PM's per hour check this quoted below posted by our admin.
Activity | Min. seconds between post actions | Max PM recipients | PMs per hour |
0 | 360 | 3 | 5 |
16 | 74 | 5 | 30 |
30 | 60 | 5 | 60 |
60 | 30 | 5 | 60 |
100 | 12 | 10 | 120 |
200 | 10 | 15 | 120 |
300 | 8 | 20 | 120 |
I hope that the above quoted could help you to get an idea.
Anyway, upgrading to copper member could increase your interval limit for pm's and posts.
https://bitcointalksearch.org/topic/m.25872334
If OP will purchase Copper Membership he will be able to send up to 40 PM's per hour/ 120 PM's per day.