I think you'll find that by and large that all circling MDA's for a particular aerodrome will be the same... i.e. even if an ILS S-I minima is dramatically lower than say the NDB-A... its (ILS) circling minima will usually be the same as other circling approaches for the same aerodrome.
There is nothing legally stopping you from doing a S-I approach and deciding later to switch to a circling maneuver provided you meet all of the circling conditions (On track until inside the circling area with vis >min along intended flight path with approach end of rwy in sight and above MDA until on normal descent profile). Doing this can enable landing in lower visibility but requires a higher cloud base... however you need to assess the risk of unnecessary circling.
The company I work for actively discourages circling unless there is no S-I approach or it is VMC by day.