Is there a limit to which an actor can improvise his/her role?

No, there isn't. It just depends on how much breathing space a director gives the actors. The director Mike Leigh actually has actors improvise whole films. He has a general plot outline, but none of the dialogue is scripted. (Ironically, he got nominated for a best screenplay oscar last year, even though he hadn't used a script- they just recorded what the actors said afterward)