And this is covered by the Magic 2015 Release Notes:
* Each additional time The Chain Veil’s last ability resolves will allow you to activate a loyalty ability of each planeswalker you control an additional time. For example, if you activate The Chain Veil’s last ability, untap it, then activate it again, you can activate a loyalty ability of a planeswalker you control three times that turn.
If you manage to activate The Chain Veil's ability twice in one turn, you'll be able to play up to three loyalty abilities of each of your planeswalkers.
Nathan Long
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