Acquiring a non-100% stake with CEO staying on

I wanted to pick your brain on a non-traditional, more PE-like transaction structure for a search fund: For example acquiring a 51-75% stake, with the CEO staying on and the searcher assuming either a non-operating role (thus contributing with growth capital and strategic advise from searcher and operating partners) or an operating role, such as M&A (if e.g. roll-up thesis) or a CRO/deputy CEO role or even CEO role with the existing CEO assuming a different role.

In my view, keeping the CEO and acquiring a smaller stake will imply:
+ significantly less operating risky given no ownership succession
+ less execution risk in transaction (given CEO not letting go of his/her baby)
+ still room for operational improvements
+ less focus on transaction price in acquisition phase (emphasis on partnership and value-add) and potentially more aligned interest
+/- opportunity for larger business, although that will come with higher price/multiple (lower FCF yield)

What are your thoughts?