I don't see it.
You're getting 3 swift actions per round (1 from corset, 1 from borrowed time, and 1 normal), but only one of those can be used to cast a spell, so still only 2 spells per round, with 2 extra swift actions to do other stuff.
I'm assuming you're casting the mythic version of borrowed time to regain the move action you sack to the corset.
Arcane surge: doesnt grant an extra swift action, it allows you to cast a spell as a swift action without using a spell slot.
Corset: swift action specifically states that you cannot use it to cast a spell - which is what Arcane surge does, so no using arcane surge twice per round.
You want to challenge your mythic PC's?
Give the big bad a mythic spell-casting cohort (perhaps with the same set-up so that they're both casting 2 spells/round)...wanna really cheese it out? give the cohort the leadership feat and a mythic spellcasting cohort of it's own.
Anyways, that's what I think.
Normal cast (spell 1)
Quicken cast (spell 2)
Familiar spell (spell 3)
Quicken familiar spell (spell 4)
Contingency spell (5).
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Mythic haste gives an extra standard action for an extra spell. Unless you sensibly nerfed it.
I don't see any reason that arcane surge should let you bypass the restriction of one swift action spell per round.
Arcane surge allows you to cast a spell as a swift action. The language "cast a spell" is even part of its rules text. The casting time rule limits you to one swift action spell per round, and does so using fairly general language. I don't see any reason why arcane surge shouldn't fall under that.
I don't see how do you not read cast a spell as a swift action as casting a swift action spell?
Anyways, I said how I interpret the wording, you obviously read it differently. Since you're the DM in this particular game, your opinion is the only one that matters, So I'll just agree to disagree with you on this point and wish you good luck with your game.
Mythic haste gives an extra standard action for an extra spell. Unless you sensibly nerfed it.
Mythic Haste grants an extra move action, not a standard action.
What you want is
Dual Initiative (Ex)
The monster gets two turns each round, one on its initiative count and another on its initiative count – 20. For example, if the monster’s initiative is 23, for its first turn it could make a full attack (and take a 5 foot step) at initiative 23, and for its second turn at initiative 3 it could take a move action and cast a spell. This allows the monster to perform two actions per round that normally take an entire round, such as using a summon monster spell. For the purposes of spells and effects that have a duration of a round or longer or trigger at the beginning of the creature’s round or the start of its turn such as saving throws against ongoing effects or taking bleed damage), only the monster’s first turn each round counts toward such durations.
Format: +21/+1; Location: Initiative.
I'll never match the rules lawyers for rules. But I can say that a mage and his familiar and his shadow and the familiar's shadow, and another shadow and the shadow's familiar... you get the idea.
Of course, when you summon, call or gate creatures in, they can each cast their own spells as well. It's not so much the caster casting 4 times a round, but it's effectively just as powerful.