A PE co is buying into our business (with a similar stake) with participating pref shares. Does their follow-on money have to be pref shares?

They are happy we can get money elsewhere if needed, but there is an obvious benefit in them providing extra funding in terms of saving time exploring the market for this. They've already got a very great deal, we're growing fast but this now feels misaligned. If we are raising extra $$$$, then we'd have to spend time and energy looking to other investment routes for non-preferred shares with better terms which will slow the business down and affect all parties when it's better to agree to this now at the outset. None of the existing shareholders are really happy about this, obviously, as we all would suffer. So, the motivation to raise more money with them for added activity gets muted. Surely their investors got a one-time preferred share deal and they don't have to get the same preferred shares over us if investing further? Thank-you in advance for any recommendations. Very much appreciated.