Always Possible Stat Boosts

• +1/+1/+1 from Basic Humanity
• +4/+4/+4 from Skill Upgrades
• +1 Muscle from "St. Polycarp's Forehead" perk (St. Polycarp's Cathedral quest)
• +1 Mysticality from "Skeptical" perk (pay for a tarot reading three times at Ocean City Boardwalk)
• +1 Moxie from "Expert Sitter" perk (Marvin's quest)

• +1/+1/+1 from wearing the completed Monster Club sash accessory (complete all Monster Shack quests). To my knowledge, it is impossible to lock yourself out of this quest.
• +1 Moxie from the "Perfect Teeth" perk (the dentist at the Maize Maze in Gray County)
• +1/+1/+1 from giving prisoners Chiropractor gift certificates (Charlestown State Pen in Government Valley)
• +1 Muscle from the "Well Adjusted" effect using the same gift certificate for yourself

• A hat and pants combo can get you +1/+1/+1 any playthrough. The intimidating Stetson from Haim Quarry in The Big Moist with S.I.T. kitchen britches from the S.I.T. gift shop) is the earliest available combo, but you can also combine any puckwudgie hat from Gray County with the corresponding S.I.T. pants from the S.I.T. gift shop). There's also the glorious tiara from the Wreck of the Longerfellow, which is difficult to reach.
• The electrical orb on your bookshelf from Radio Shack in The Big Moist grants +1 to your class' main stat when you touch it.
• The statue of you from Puckwudgie Village and one of the three M-stat cats (not counting the dream cat) can grant you +1 to an additional 2 M-stats
• Finally: Losing battles (NOT surrendering!) will grant you Angry), Contemplative, and Aloof effects for an additional +1/+1/+1.

Bridging the final +6 gap

Dreams

• The Dream Cat from the Prologue grants +1/+1/+1, for an additional +2 M-stats compared with the other M-stat cats. They are very missable, and you can permanently lose their boon if you pet another cat on Chapter 6, as you will not go to sleep again.
• You must complete quests in your first four dreams to get the perk Pep talk, granting +1 to 2 of your 3 M-stats. You choose the M-stats by picking which statue to silence in Yet Another Fitful Dream.

Clothing

• The giant maggot hat, which comes from helping the miners and NOT working with Frogger at Haim Quarry, gives +1/+1/+1 for an additional +1 M-stat.
• Weathered Jeans can be bought from Advanced Pants on Day 4 if you choose it as an additional shop on Plunkett street. It grants +1 Muscle and +1 Moxie, and is the only pair of pants to provide +1 to more than 1 M-stat, for an additional +1 overall. You will only install 5 of the 9 possible stores on Plunkett street during a playthrough, making it easy to miss this shop.

Food

• Any food starting with H can be thrown in The H***hole in Gray County to make devil's food cake, for +1/+1/+1. Of particular interest are hot links, which can be crafted at arcane ovens from the infinitely abundant phlogistic resin. This is always available in any save file, but easily missed.
• The Dauphin House) in The Big Moist contains a Can of Fruit Cocktail for +1/+1/+1. This item is unique.
• Fruit Advertisements can be gotten from Junk Mail once you've gotten the letter opener on day 6. They give +1/+1/+1 when eaten.
• Fish sandwiches can be bought from Fission Chips or The Underground Restaurant) for +1 to 2 M-stats of your choice (suboptimal, but available starting day 3)
• Finally, picking Botany as a major opens up 2 interesting options for an additional (suboptimal) +1 to your M-stats: You can make a questionable salad at Professor Kalos' Holiday Home which grants +1 to Muscle and Mysticality when eaten, AND you can wander at S.I.T. with Barker to find Odd Fruit for +1 to Muscle and Moxie.

Potions

• The Noble Exlixir (+1/+1/+1) will be sold at Ye Olde Chemicker if you install it on Plunkett Street, but ONLY on day 6. You will only install 5 of the 9 possible stores on Plunkett street during a playthrough, making it easy to miss this shop.
• If you take the Chemicals major at S.I.T., you can get Professor Adams as a companion. Talking to him at Ye Olde Chemicker will give you 3 of Professor Adams' special potions for +1/+1/+1. This can only be done once, but can get you +1/+1/+1 potions before day 6.
• Without Ye Olde Chemicker, you can find radium rouge at the Dauphin House in The Big Moist for +1 to Mysticality and Moxie (suboptimal). This item is unique.

Other

• At The Old Junkyard at Crystaldream lake, there's a tub you can soak in for +1/+1/+1 for the rest of the day. This is a one day only effect; you can only soak once and will not be able to soak any other day. Optimal to soak on day 6.
• Similarly, in Gray County, you can encounter a blob of crude oil surrounded by electrified shale spires. If you choose the option "Harness the Lightning [7 Mysticality] you get +1 Mysticality from the Fossil Fueled effect for the rest of the day. This option can only be chosen once; the event can occur many times, but once you choose to harness lightning, it will never happen again (optimal to do so on day 6).
• Finally, the exploit: You can get +3/+3/+3 if you choose spiders as an elective at S.I.T. I don't recommend it, but it's there.

Bonus Guide to Liquors