The MLA Handbook (8th ed.), 1.3.7, says:
Do not use opening and closing quotation marks to enclose quotations set off from the text, but reproduce any quotation marks that are in the passage quoted.
In "Memories of West Street and Lekpke," Robert Lowell, a conscientious objector (or "C.O."), recounts meeting a Jehovah's Witness in prison:
I was so out of things, I'd never heard
of the Jehovah's Witnesses.
"Are you a C.O.?" I asked a fellow jailbird.
"No," he answered, "I'm a J.W." (36-39)
By "set off from the text," it means a block quote, which has a left-margin indent.
Notice that it uses a block quote for the lines of text, and then provides the citation (36-39), which, in this case, is citing line numbers rather than page numbers because "Memories of West Street and Lekpke" is a poem.
It does, however, provide a different style where a block quote is not used:
Use double quotation marks around quotations incorporated into the text and single quotation marks around quotations within those quotations.
In "Memories of West Street and Lekpke," Robert Lowell, a conscientious objector (or "C.O.)", recounts meeting a Jehovah's Witness in prison: "'Are you a C.O.?' I asked a fellow jailbird. / 'No, he answered, 'I'm a J.W.'" (38-39)
Notice the difference in quotation marks when no block quote is used, and how a slash (/) character indicates a line break in the poem. A stanza break would be indicated by a double slash (//).
MLA, 1.3.3, says this about poetry:
Verse quotations of more than three lines should be set off from your text as a block.
For quotes of prose, MLA 1.3.2 says:
If a quotation extends to more than four lines when run into your text, set it off from the text as a block indented half an inch from the left margin.
I would certainly use a block quote for your example text. If nothing else, it simply looks better.
In The Great Gatsby is the following exchange:
'An Oxford man!' He was incredulous. 'Like hell he is! He wears a pink suit.'
'Nevertheless he's an Oxford man.'
'Oxford, New Mexico,' snorted Tom contemptuously, 'or
something like that'. (50)
The (50) I used in that is just an arbitrary page number I made up.