I was tempted to suggest the narrow staircase at Stourport - but it is the upper chamber that has the side weir, presumably to regulate the basin.
The first lock on the Wey, with the additional gates sometimes used to lift boats over the cill is an example - but not a conventional one
Putting aside 1st Ade point about differing lengths/widths, the use of a staircase will tend to move the two rises towards each other. I.e. if the top lock has an ostensibly greater rise, when its contents are discharged into the lower chamber it will leave the level higher than the bottom of the coping stones - and the top chamber will not be as low as otherwise. There shouldn't be an issue on draft over the lower cill. But if the masonry is insufficient to accept half the total rise, it will be overtopped.
So the hydraulic rise will always be the same for each chamber (assuming other factors remain constant) - and the masonry etc needs to allow for it, and a little bit more for canal level changes etc.
Incidentally the same applies to a canal which, in concept is one long staircase until the summit/sump is reached. But there are a lot more factors in play in the longer pounds - with weirs, inlets, boats changing defections, pairing up etc. The effect is more obvious on short pounds which rise and fall as adjacent locks are drawn