Specifically, they said they wanted the Munich-based firm to rethink the management structure that was put in place at Pimco after El-Erian's departure. The new configuration has six deputy chief investment officers (CIOs) under Gross. They also want assurances on Gross's pay and a detailed long-term plan on how Pimco plans to broaden its focus beyond fixed income.
Allianz, which has said little publicly about Pimco's performance or the internal disagreements at the fund manager, declined to comment.
Douglas Hodge, who replaced El-Erian as chief executive of Pimco, told Reuters on Thursday that the California group has spoken to "literally thousands" of its clients and that the vast majority are comfortable with the new structure.
Read MorePimco's Bill Gross has company in bond misery
Over the last five years, Pimco points out, it has launched over 150 new investment funds across multiple platforms including private equity, hedge funds and active equities asset classes.
The critics say the developments of the past months suggest Gross has been given too much freedom. Investors pulled $3.1 billion from Pimco's flagship Total Return fund in March, the 11th straight month of outflows from the world's largest bond fund, and its performance on the month lagged 95 percent of its peers, fund data firm Morningstar said this week.
"The leash is obviously too long because there is a performance issue now," said one top-10 investor. "A fully owned subsidiary should not be run like this."
A second top-10 investor said it was considering attending the Allianz AGM for the first time in years in order to raise questions about governance at Pimco that it feels need to be addressed in public.
If the shareholder does take this step, it would be an unusual move in Germany, where big institutional holders usually voice their concerns in private.
Read More Damage control at Pimco after Gross, El-Erian clash
The three critics, which together hold less than 10 percent of Allianz shares, said they were still assessing whether private meetings with Allianz would be sufficient to alleviate their concerns.
"For us performance is the issue, not the battle between Gross and El-Erian," the third top-10 critic said.