Here's a potentially interesting objection to limited atonement:
Three theories of atonement are particularly used. The Acceptilation theory of Duns Scotus, which determines the meaning of the cross from the extrinsic acceptatio of God, is used to ascertain the value of Christ's work from the will or intention of God [e.g. John Owen, Francis Turretin]. The Satisfaction theory of Anselm is employed in asserting that Christ through his death merited "faith, repentance, and the Holy Spirit" for the elect" [e.g. Turretin, J. Heidegger]. The Penal Substitution of Luther is used to decry the "double jeopardy" of unlimited atonement, since the cross, having punished sin and therefore satisfied divine wrath, must save within itself and require no further punishment or satisfaction [e.g. Owen, Turretin, J. Heidegger].
The difficulty in employing such divergent theories of the atonement can be best illustrated through the oft-repeated phrase that the death of Christ is "sufficient to save all men," but due to the intention of God is "efficient for the elect alone"–a phrase used by proponents of both limited and unlimited atonement. Initially Christ's work is interpreted here through the theory of Anselm, a theory which exults in the intrinsic "sufficiency" of his sacrifice and infinite dignity of his person, but then it is immediately overturned by the extrinsic consideration of the divine will, which according to Duns subjugates the "efficiency" and merit of Christ to the acceptation or ultimate intent of the Father. How can anything be inherently infinite in dignity and then be limited in value before God? Are Christ in his works and the Father in his will opposed? Stephen Strehle, "The Extent of the Atonement and the Synod of Dort." Westminster Theological Journal (1989), 1n1.
How should we assess this objection?
i) Strehle isn't making a case for the Amyraldian alternative. Indeed, he thinks that operates within the same flawed framework–as he explains later on.
ii) Although he says these are "divergent" theories, he doesn't explain how the satisfaction theory and the penal substitutionary theory contradict each other. Even if these two theories developed independently of each other, they may be conceptually harmonious.
iii) His specific example is how the acceptation theory allegedly contradicts the satisfaction theory.
iv) I do think the language of "infinity" is ambiguous.
v) On the face of it, it's easy to come up with counterexamples in which something that's intrinsically efficacious can be limited in application. Suppose you have an efficacious antidote for snakebite. Yet you are free to selectively administer the antidote to some patients to the exclusion of others. Suppose a member of the Medellín Cartel is envenomated by a Bushmaster. You could save his life by administering antivenon, but because he's responsible for torturing and murdering innocent people, you have no duty to save his life, so you administer a placebo instead.
Perhaps Strehle would say that's not analogous to the kind of intrinsic/extrinsic distinction he's drawing. If so, his objection, as it stands, is too vague to demonstrate that these are divergent theories of the atonement.