go all the way with this

[GoldfishLord]

Alexei Stukov: So. Gerard, I suspect you have a good reason for pulling me away from my... duties.
Gerard DuGalle: Your vodka can wait, my good Alexei. Come, stand here. You need to see this.
Alexei: I know all about the Zerg, Gerard. We've all seen the tapes a hundred-
Gerard: You've seen nothing! Dissecting a dead Zerg in a lab is one thing. Unleashing them on man is another. You must go into this with both eyes open. Once started, there is no going back. Are you prepared to go all the way with this, Alexei?
Stukov: Yes...Yes I am prepared to go all the way, my good admiral.

Source: https://starcraft.fandom.com/wiki/StarCraft_campaign_quotations

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Does "with" mean "despite" or does it mean "in the company or presence of something"?

 

[White Hat]

I think it actually means 'on' ('on this'). Like here: "I want to go all the way on this."

 

[5jj]

go with something

[...]
2. to agree to accept something, for example a plan or an offer

• You're offering £500? I think we can go with that.

go with phrasal verb - Definition, pictures, pronunciation and usage notes | Oxford Advanced Learner's Dictionary at OxfordLearnersDictionaries.com

Definition of go with phrasal verb in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.

www.oxfordlearnersdictionaries.com

 

[GoldfishLord]

Does the "all the way" in "all the way with" mean "to the fullest and most complete extent"?

 

[5jj]

Yes.

 

[Barque]

Does "with" mean "despite" or does it mean "in the company or presence of something"?

"With" never actually means "despite", though it might effectively mean that sometimes.

Here, he's asking Are you prepared to go all the way as far as this matter is concerned?
Or: Are you prepared to go all the way as regards this matter?