In this question Explicit Bezier Curves: Lerping between curves same as lerping control points?, it shows that linearly interpolating between the result of evaluating two explicit bezier curves is the same as interpolating between their control points and evaluating the resulting curve.
Where an explicit bezier curve is defined as below, $A,B,C$ being scalar constants. $f(t)=A(1−t)2+B(1−t)t+Ct2$
Are there any other interesting operations which could be applied to the result of evaluating those two curves which is equivalent to performing the same (or similar) operation on the control points themselves?
Lerping being one such operation, I'm looking for other operations, such as scaling, rotation, projection, or anything similarly useful.