You can only spend 1 surge per attack to recover strain. However, there may be other abilities which will let you recover more than one strain per attack. For example: Davith's "Elusive Agent" 1XP card says "Exhaust this card when you become hidden to recover 1 strain". So If Davith has 2 surges during attack, he can spend one surge to get hidden--> Exhaust Elusive Agent to recover 1 strain and another surge to recover strain.
Notice that Elusive Agent is Exhaust, so Davith will only be able to recover 2 strain only once during his activation by spending surges like above.