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Talking about Mythic: 2° tier common ability:

Amazing Initiative (Ex):

At 2nd tier, you gain a bonus on initiative checks equal to your mythic tier. In addition, as a free action on your turn, you can expend one use of mythic power to take an additional standard action during that turn. This additional standard action can’t be used to cast a spell. You can’t gain an extra action in this way more than once per round.

And then the Champion feature says:

Sudden Attack (Ex):

As a swift action, you can expend one use of mythic power to make a melee attack at your highest attack bonus. This is in addition to any other attacks you make this round. When making a sudden attack, you roll twice and take the better result, adding your tier to the attack roll. Damage from this attack bypasses all damage reduction.

Can I stack both? My head says Yes, but Im not sure and then:

At least at 19° level, with 4 mythic tiers, a 2-hand-weapon fighter and Champion can do each round: 4 normal attacks + 1 "haste" attack (from boots or other) + 1 attack from Amazing Initiative (1 Mithic power used) and +1 from Sudden Attack (2 Mythic power used) =7attacks.

Can I say: all of this is correct? Cause it's a bit confused to me but I'm not english native.

Aren't 2 questions cause the first question can delete the latter. Thanks

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Yes, you can do both.

The restriction on Amazing Initiative restricts you from gaining additional Actions, not from gaining extra Attacks, and further, it is only limiting you from using Amazing Initiative to gain additional actions more than once per round, and has no effect on any other method of gaining more actions.

Sudden Attack lets you make an attack as a swift action. Instead of giving you an additional action, it lets you use your swift action for something you normally couldn't use it for, so it would be unaffected by the restriction from Amazing Initiative anyways.

So, if you were to be under Haste, and spend two uses of Mythic Power, you could indeed make 7 attacks. 4 at Full BAB (primary attack, Haste attack, SA attack, and AI attack), one at BAB -5, one at BAB -10, and one at BAB -15.

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    \$\begingroup\$ It's worth noting that this is a tame application of Mythic rules compared to some of thing things you can do with them... \$\endgroup\$ Commented Dec 21, 2020 at 20:57

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