Yes, cf. p. 127 of the Klingon Core Rulebook.
My interpretation is that you simply insert another link into the chain.
Let’s take for example, ta’vanaH (Tavana), daughter of 'a’Setbur (Azetbur), proud warrior of the honourable house of Do’ran (Doran) who is serving as commander of one of the bird of preys of her house. She has the value Honour before everything! which (most of the time?) lets here choose the honourable path over the easy one. Let’s follow her over the course of her adventures.
Adventure 1: While on an errant in a different affair, Tavana notices a cowardly assassination attempt in a dark back alley. She decides that it would be unhonourable to witness a cowardly assassination attempt, doing nothing, steps in and fights of the assassin, using her Value positively.
She notes V1+ next to the log entry.
Adventure 2: Following the trail of the assassin, later, she discovers that he belongs to the house of tlha’veq (Klavek), a mighty and well-renowned house. Despite this will make herself and her house an enemy, she decides to speak up against the house, using her Value negatively, while calling back to the assassination attempt in adventure 1.
She notes V1- next to the log entry, ticks the log entry of Adventure 1 as used (and maybe she also notes A1 next to the entry for Adventure 2 to indicate that this ties back to Adventure 1). Doing so grants her the effect of a Milestone.
Adventure 3: During the adventure, the house of Klavek takes their revenge, pulling strings and isolating the House of Doran and forcing them to take back Tavana’s accusations. Azetbur, both leader of the house of Doran and Tavana’s mother, begs her to stand down as keeping up the accusations against the house of Klavek would endanger the lives of everyone within the house. Tavana is enraged but ultimately complies and revokes her accusations, challenging her value and calling back to adventures 1 and 2.
She notes V1! next to the log entry, ticks the log entry of Adventure 2 as used (and maybe she also notes A2 next to the entry for Adventure 2 to indicate that this ties back to Adventure 2). Doing so grants her the effect of a Character Arc. She also rewrites her challenged value to First my House, Second my Honour, Third: all else.
Adventure 4: Tavana wants revenge, but, according to her second Value Revenge is a dish best served cold, she can wait. She is given the opportunity to safely expose a minor servant of the house of Klavek, but uses her value negatively and does not strike.
She notes V2- next to the log entry.
Adventure 5: Still looking for revenge, she dives into the dark doings of house Klavek. Now she finds that the commander of one of their battleships is involved in smuggling. Again, using her value negatively and calling back to adventure 4, she waits, uses the information to delve even deeper into Klavek’s secrets.
She notes V2- next to the log entry, ticks the log entry of Adventure 4 as used (and maybe she also notes A4 next to the log entry of adventure 5 to indicate that this ties back to Adventure 4. Doing so grants her the effect of a Milestone.
Adventure 6: Even deeper, another crime of the house of Klavek uncovered: A different commander is secretly dealing with Romulan spies. While this would be enough to severely damage the houses reputation, when uncovered, Tavana waits, calling back to adventures 5 and four, and, again, using her value negatively.
She notes V2- next to the log entry, ticks the log entry of Adventure 5 as used (and maybe she also notes A5 next to the log entry of adventure 6 to indicate that this ties back to Adventure 5.
Doing so would, in principle, grant her the effect of a Character Arc, but since she already had one arc, there is no effect (not taking into account the regular effect of a log entry, that is).
Adventure 7: Finally! Tavana is able to uncover that the leader of the house of Klavek is secretly plotting with the infamous house of Duras. Calling back to adventures 4, 5 and 6, she uses her value positively to boost her speech before the Chancellor Martok and the Klingon High Council to make sure the house of Klavek meets its fate.
She notes V2+ next to the log entry, ticks the log entry of Adventure 6 as used (and maybe she also notes A6 next to the log entry of adventure 7 to indicate that this ties back to Adventure 6).
Having now completed a string of, in total, 4 adventures connected by a single value now grants her the effect of her second character arc.
Now, Tavana had challenged and rewritten her first value. In case she would have, in parallel to adventures 4–7, a second arc revolving around this, uncovering that some of her own familiy members secretly work with the house of Klavek (or doing other dishonourable acts, maybe?), she could build up a second arc in parallel to the one described here.
Whichever arc would be finished first with its fourth adventure would automatically prolong the other arc by one adventure.
The only thing that is not clear to me now is the following:
The third arc will need a total of five adventures:
- regular log entry: starting the arc
- getting a milestone
- regular log entry: prolonging the arc (would be the place for first arc milestone)
- regular log entry: prolonging the arc (would be the place for second arc milestone)
- getting an arc milestone
Will there be a milestone at the fourth adventure of the third arc? Or will adventures prolonging the arc simply grant the effect of a regular log entry? To me, the rules seem to be silent, resulting in the latter.