bungfai,
there are 2 factors that affects your Max Alt. One will be your aerodynamic limit i.e. 1.2G, etc. the other factor will be your engine thrust!
for 4-engine airplane usually the Max Alt is govern by the aerodynamic limit. this is where you hear about the 'coffin-corner'.
for 2-engine airplane usually the Max Alt is govern by engine thrust. this means aerodynamically your airplane can actually go higher to reach the 1.2G limit but unfortunately, your 2 engines can only produce that much thrust at that altitude i.e. 300fpm.
what speed? well, it depends what you enter in your FMC. if you change the CRZ speed, the Max Alt will change. so whatever speed you entered in your FMC, at that Max Alt and CRZ Speed, you will only get 300fpm at your max. CLB thrust (this is for the B777). if you do not have your FMC, then the QRH will give you the Max Alt at LRC at different ISA.
as i've said above, for most instances, for a 2-engine airplane (B777) you will most likely be residual climb rate limited.
hope this clears it up for you?
SR