They don't make a EVSE with such a mode nor do I see they ever will but I do it all the time. My EVSE has a 20a and 30a setting and when I need to I use the 20a setting(actually pulls 19a which is good) and of course 30a is limited to 27.5a by the Leaf.
Note while you can generally pull full load amps for a short period of time after about a half-hour things will get very warm, things like the breaker(you can actually feel it) and even the blades of the plug, I'm sure the socket is very warm also but you can't really feel that. You also need to know your outlets and wiring are up to snuff, a weak or old outlet and things could go from very warm to HOT which is NOT good. You can't really feel things like wiring, especially behind the wall but you might be able to feel it near the breaker panel, warm is OK but NOT HOT.
If you want to play around with maxing your circuit I'd suggest an EVSE like Juicebox that lets you set the current draw down to the amp, start at 80% and gradually start increasing your draw by an amp, then keep a close on eye on things by feeling the plug and wiring if you can, also feel the breaker. Again warm is ok but not hot. Once you find a good max setting you'll have to manually stop charging, automating it would be rather complicated and again your not going to find an EVSE that does it automatically.
2012 SL purchased used 2/'16
2013 S w/QC purchased new
Juicebox Premium 60a L1/L2 EVSE, Ebusbar 16a L1/L2 EVSE
'12 EVSEupgrade'd 20a L1/L2 EVSE, '13 EVSEupgrade'd adjustable 6-20a L2, 6-13a L1 EVSE
Zencar 13, 20, 30a L1/L2 portable EVSE
GE Durastation 30a