Can you take an immediate action while you're delaying?

[B. A. Robards-Debardot]

Byakko wrote:

Otherwise you'll wind up with silly situations where a bard with highest initiative could delay all the way from the top of the initiative order to the bottom and still maintain their song, but a bard with lowest initiative couldn't delay even one spot.

With your methodology, neither of the Bards would be able to delay and maintain the performance.

Higher initiative comes with perks, which the delay action maintains.

When you Delay, you have 3 options.
1) Enter initiative in the same round at a lower initiative count.
2) Lose your turn for the round and begin at a higher initiative count the next round.
3) Lose your turn and begin at your previous initiative count.

Typically, most people are better of acting in a round then not acting in a round, so if you've delayed until the end of the round, you should probably act. Even if in this case it is to maintain the performance and then complete or ready actions.

[Byakko]

That's an archaic way at looking at rounds, and the rules verbiage really needs to be updated. Losing your turn at the end of the global round and regaining it at the start of the next is effectively the same thing as just delaying without any mention of global rounds at all.

There's no real difference between acting last in a global round or acting first in the next. (with the exception of the surprise round)

If you're a bard, you technically can't delay and continue to maintain your performance.
However, for the sake of ease of play and continuity, most GMs are willing to fudge this a little to allow it to make sense.