Recruiter: "Here's your offer for $X compensation."
You: "I was actually looking for something paying $X+Y."
Recruiter: "Well our offer is $X."
You: "This data shows that comparable jobs with the work I'm taking on are paying $X+Y."
Recruiter: "Our offer is $X. Do you want the job or not?"
You: "Well, I'm not willing to join for less than $X+(Y/2)."
Recruiter: "OK, well, bye. We have 35 other candidates lined up to talk to. Good luck."
Not sure how it's different when you have multiple offers. The company offering a lower comp will just say "Well, their offer is higher. Have fun at Company B. Thanks for interviewing!" Reading stories of these Captains Of Industry just asking for more and getting it, or getting companies into a bidding war over them is... kind of wild. It's like we're living in different universes.