Well, if Plato's 36 works need a 'tetralogy' classification to help create a map of his output, then surely something similar should help understand Shakespeare's outputs, which typical complete works would count his 36 plays included in the First Folio, 2 other plays, 4 poems and a set of hundred some sonnets. Altogether 43 works if the Sonnets are considered one unit.
In the First Folio, Shakespeare's works are classified as Comedies, Histories, and Tragedies; and then scholarship typically talk about Late Romances, and Problem Plays. While the chronology of Shakespeare's outputs is actually clearer than Plato's, the chronology is not firm. Therefore, as I seek to classify Shakespeare's work, I propose that we can also use some simple parameters about the dramatic settings as classification criteria.
So below are my scheme:
I. Italian/Spanish Comedies (5 works) - these tend to be earlier comedies. I don't have a strong view about how these should be ordered.
- The Two Gentlemen of Verona
- The Taming of the Shrew
- The Merchant of Venice
- Much ado about nothing
- Love Labour Lost (the setting of this is in Spain, the others are in Italy)
II. Other Comedies (5 works) - tend to be later / "high" comedies. Also in a set of 4+1 with the odd one being set in UK and actually and offshoot of his Histories. Again, I have no strong views on the ordering.
- The Merry Wives of Windsor (this is the offshoot from Henry IV)
- The Comedy of Errors
- Midsummer Nights Dream
- As you like it
- Twelfth Night, or what you will
III. Major Histories -- in a set of 1+4. This covers the earlier time period in English history, but tends to be written later than the next set of histories. Ordering is chronological based on the historical period the plays cover.
- King John (this is like a prologue, timed outside of the tetralogy that follows)
- Richard II
- 1 Henry IV
- 2 Henry IV
- Henry V
IV. Minor Histories -- again in a set of 4+1. Tend to be written early, but period it covers are later. Order is again chronological of histories they cover.
- 1 Henry VI
- 2 Henry VI
- 3 Henry VI
- Richard III
- Henry VIII (this is like an epilogue outside of the tetralogy in this set)
V. Ancient Tragedies -- these tragedies are set in ancient Roman / Greek time. 4 in Roman Empire/Italy, and one in Greece. There really should be an order, but I haven't looked into these deeply.
- Titus Andronicus
- Julius Caesar
- Anthony and Cleopatra
- Timon of Athens (this is set in Greece)
VI. Major Tragedies -- this is set in post-ancient Europe. Can consider it as a set of 1+4, since the term "4 major tragedies" seem to be in common parlance already
- Romeo and Juliet (this is the non-major one)
- King Lear
VII. Problem Plays (3 works). If the groupings are 5-each and total number of works is 43, there got to be a group that just has 3 works.
- Troilus and Cressida
- All is well, ends well
- Measure for Measure
VIII. Late Romance. This is probably like a set of 3+2, with 2 late plays written in collaboration with others, and also not included in the First Folio
- Winter's Tale
- Pericles (not in First Folio)
- Two Noble Kinsmen (not in First Folio)
IX. Poetry. Even this is in a set of 4 poems +1 set of sonnets
- Venus and Adonis
- The Rape of Lucrece
- To the Queen
- Let the Bird of Loudest Lay
This classification still retains most of the First Foliio's distinction of Comedies, Histories, Tragedies, and I think is a handy way to remember the works and what genre they are in. In terms of reading order / priority, clearly the works in VI Major Tragedies including Hamlet, Lear, Macbeth, Othello, Romeo and Juliet are the most important. From the other categories, for Comedies, II is more important with Midsummer Night's Dream and Twelfth Night. For Histories, III Major Histories is more critically acclaimed, and if I choose one work I would choose Richard II as it kind of officially starts the sets of 2 trilogies. And for problem plays / late romance Tempest should have the pride of place as it is both the first work to be included in the First Folio, and the last solo work by Shakespeare. (It is officially counted as a Comedy too in First Folio's classification). So this is a short-list of 9 plays out of 38.
To further whittle down to a 5 works, for me the selection probably should be the 4 Major Tragedies (ex-Romeo) + Tempest.