Is it acceptable, as a Reviewer, to ask the Editor about another reviewer?

I have a very simple solution to propose:

• Write a message directly to the other reviewer whom you would like to know. Address it to the reviewer, not to the editor.
• In the message, identify yourself and give your contact information. Ask the reviewer to contact you if they are interested.
• Send that message to the editor and ask the editor to please transfer it to the other reviewer, either immediately, or later in the review process (perhaps after a decision is made) when the editor feels comfortable doing so.

Note one important difference from what you ask in your question: rather than asking to be able to contact the reviewer directly, you are asking the reviewer to contact you. This is a very important difference because it gives other people more choice in the matter.

The editor will either transfer the message to the other reviewer (either immediately or after a decision is made, perhaps after you have sent a reminder) or will explain to you why they do not feel comfortable with your request. The advantages of this proposal are:

• There is no moral concern because you do everything openly before the editor; you even show the editor the contents of the message, so the editor has no concern of anything improper going on.
• You give the other reviewer the choice if they are comfortable with the contact. If they are not, the editor has not divulged their information to you. This relieves pressure from the editor.
• You leave the editor free to judge the appropriateness of the contact. So, it is not your responsibility, but the editor's.
• Even if the editor decides not to give you the reviewer's contact information, the editor should be able to respect that your intention was sincere, your approach was transparent without pressuring anyone, and the editor should not have any negative impression of you.

I've never encountered this. My inclination would be to ask the other reviewer if they're OK with the request. If they decline, then that would be final. After all there is usually nothing stopping a reviewer from identifying themselves if they wish; I certainly know of people who gave away their reviewer duties during private conversations.

It probably won't hurt to ask, because the worst that can happen is the editor says "no". If you do ask, I would definitely give the reason, since otherwise it's rather suspicious. You may also have to reveal your own identity first.