Li-ion battery applying more current
You 'can' indeed charge li-ion cells faster that they are rated for. 
If can means is it possible, yes. 
If can means, is it totally fine, then no. 

When the battery is charging or discharging there is a transfer of charge at the electrodes. The charge concentration at the electrode then diffuses throughout the rest of the battery. This does not happen in an instant. It takes a different amount of time for each battery, hence batteries having different ratings.  

So what happens when we do not allow for enough time for that battery to diffuse the charge concentration at the electrodes? You get lithium plating occurring at the electrodes; this is permanent. Enough of this and your battery will perform badly, if at all.