No.
Anger management: If I am in a rage, or an Unchained rage, or a bloodrage, or some similar form of rage, can I stack up as many benefits as possible?
No. When you either activate or are affected by a new form of rage (such as a barbarian’s rage, a skald’s raging song, a bloodrager’s bloodrage, and the rage spell), you can choose whether to keep your current rage or to accept the new rage instead, much like a creature affected by multiple polymorph effects. If you are in the throes of a rage that you could not automatically end on your own, such as a wild rager’s wild rage, you may not choose to replace it with a new rage effect. The exception to this rule is the skald’s master skald ability, which explicitly allows the skald’s raging song to stack with other rage effects.