It is possible to permanently increase stats by using special conversations or interactions with the world. These bonuses are permanent and optional to obtain. You should definitely try getting them as additional stat points will help you complete the game.
Taking up work in Manufacture - The manufacture is located in Underbelly (M4.4). Talk with the Master Foreman and suggest joining the other workers. This event will result in permanent +1 to Might.
The Sorrow's Prey - talk to Zaofi the Sculptor (M3.9) who can be found in Circus Minor. The final part of this quest involves visiting The Calm to speak with Seria. This meeting will unlock Seria's Peace, a new passive ability that offers a permanent +1 to Might, Speed, and Intellect.
Beloved Slave - Visit Circus Minor to meet up with Tol Maguur (M3.14). The quest involves retrieving Rhin, one of her slaves. The conclusion will either see you deliver the girl or convince/confront Tol Maguur to change her mind and release Rhin. In both cases your Tidal Affinity will be increased by 1.
Encounter with Aidan Sitabo - Aidan can be found at Cliff's Edge (M6.1). If you win against him in various tests of might, speed etc, you will receive 1 additional Speed point. Additionally, if at the end of the fight you decide to break the man's neck, you will obtain another point.
Conversation with Dhama of the Bloom - Dhama of the Bloom can be found in Fifth Eye Tavern at Cliff's Edge (M10.2). If you allow Dhama to enter your mind, your Intellect pool will increase by 1.
Conversation with O - You will encounter the mysterious person in Sagus Cliffs' Fifth Eye Tavern (M10.3). Using all dialogue options will increase your Intellect by 1 and Health by 4.
Finding Abtrucense - The fishing area can be found in the southern part of Underbelly (M4.11), along with a character - Crooked Qeek. She will ask you to help her fish out an item - Sparkle. This item is not the only one you may find by fishing in this area. The game will enable you to continue fishing, but the attempts should be separated with a day's rest so the chance of finding something valuable increases. After fishing, search for any location that enables you to rest. You'll find a few less valuable things at first, but those patient ones can finally fish out Abtrucense, a Cypher awarding a permanent +1 to Might.
Valley of Dead Heroes
Darkness - this strange entity can be found in the south-western corner of the map (M12.9) (left from your initial position). If you try determining the nature of the darkness and you will bind yourself with it, you will increase Intellect by 1 point.
Delivering the Phylactery - The tombs below the Necropolis are also surveyed by Silver, who will be encountered a few times during your visits to the individual tombs. He will be happy to accept the Phylactery, an item found during random exploration of the graves. One of the rewards includes asking Silver to increase your Lore: Machinery by 1. More details on how to encounter Silver and how to find the Phylactery can be found at List of Codes to Necropolis Tombs.
Canvassing the trash for interesting items - To begin, talk with Crimper, a person found in Small Nihilesh (M19.8). If you agree to search for items with the man, you'll find a mysterious cube. Repairing it results in an additional +1 to intellect, and +1 to Lore: Machinery. The right combination is as follows: remove the power supply, rotate the core, connect the power supply, lower the main controller.
A conversation with Kwherezimian - The man can be found in Small Nihilesh (M19.7). First, you'll need to speak with Aen -Tozon and help him free himself from the Maw. After that, you'll receive the opportunity to speak to Kweherezimian. The man will ask you if you can detect a person's Tide. Answer negatively to receive a permanent +1 to Tidal Affinity.
Finding the Gauntlet of Murder - (Dracogen's Price) The item is carried by Doran, the leader of a group of cultists that are encountered in Ascension (M20.2) while travelling with the Magmatic Annulet. The item can be taken from him after the fight, or simply received once you've managed to convince the man to surrender. If you equip the gauntlets, your Speed will increase by 1.
Using the Candy Dispenser - The item can be found while crossing The Gullet (the first part of Into the Depths). Visit the northern part of the map (M23.3) to find an area inhabited by a Murden. Use Concentration to eliminate the enemy and find a Candy Dispenser. Open your inventory, take a look at the new item and use it. You'll be rewarded with a Pastel Blue Candy, a cypher granting a permanent +1 to Intellect.
Bloom's Heart - the conversation with the Bloom's Heart (a part of Into the Depths (Map 24)) can result in additional +2 to Intellect. To receive the bonus, you'll need to block the Heart's aorta and calm it down. Both these actions will enable us to look into the mind of the being and acquire the said bonuses.
Note - The availability of these options is dependent on your previous decisions. There is a possibility that they may not be available.