Yep - got experioence and "It depends" is the answer.
Some institutions have mandates that are kind of "anything goes", others specify minimum buy in pricing and/or mandate removal if a stock trades under a certain dollar price over a specified time period. Some specify exchanges that holdings have to trade on, others are "no holds barred".
Generally smaller, lesser known institutions will have looser rules. If you want the real major investors, they will often have tighter rules.