No. Each fighting style uses one skill slot. Page 76 states “each fighting style uses one proficiency slot.” For clarity’s sake, this is changed to “skill slot” in the PDF.

 

When choosing “hand to hand combat” as a skill, the agent must choose one fighting style. Additional fighting styles must be learned using mission points.

Fighting styles are an exception to the tradecraft rules in that agents do not know any fighting styles until they specifically train in them. Agents who have not studied hand-to-hand combat can still fight unarmed, but receive no bonuses.