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Understanding the confusion
One of the biggest misconceptions I've seen circulating the fandom at times is this idea that only Finality is truly capable of altering the future, and that people like Elio even possess the ability to literally control the fate/destiny of the cosmos through the "scripts" he sees/"writes" when this isn't necessarily the case. Of course, it's not hard to see how this belief arises: Terminus, as one of the few Aeons to be born in the future at the "end" of the universe (like Fuli), moves backwards through time. Because of this, THEY have the unique ability to have their visions/whispers deciphered by those like Elio or the Omen Vanguards who received the blessings of Terminus to "see" those same visions, and "see" an absolute version of the future. But, this isn't always the case.
The truth, instead, lies in something known as the Solitary Waves Theory.
In Antinomic Waltz, by this point, the player had heard of Herta's infamous Solitary Waves Theory that had been her ticket into the Genius Society. In the simplest terms, the Solitary Waves Theory defines fate within HSR universe: that fate is either constant and predetermined with no free will, or chaotic and undetermined.
More than that, Herta gives us another important fact related to it: that any Path at any time can alter the destiny of the cosmos, not just Finality. By knowing this, it explains why there are so many manipulators who claim to be able to alter the fate of the universe, or the fate of a specific planet or event. From Asat Pramad to Yao Guang, fate rests not in the hands of Finality alone.
In Fu Xuan's Character Story I, her conversation with Nous also illuminates this fact. In questioning whether the future is predetermined or not depends on whether a stable constant is followed exactly, or if Paths or actions can change the outcome of any given event. Indeed, the answer is that any Path can exert the power to change the future, no matter who does it.
Examples by Path:
Of course, it's one thing to simply explain this concept as a whole when there's many examples of this in the story. Here are some I've compiled, but this is by no means a complete list.
Elation
In So Laughed the Masses, Serotonin Exposure Phobia, Asat brags about how he can change the "script", which I believe led to the initial confusion that Elation could uniquely alter fate/the "script" within the fandom recently. The reason for this is fairly clear.
In Scene 999: GAME NOT OVER, through being shown the possibilities of Silver Wolf's future that would've come with the uninhibited use of her lvl 999 Cartridge, we're told that the unpredictable power of Elation has the power to interfere with the "script"/Finality.
Over a year ago in Antinomic Waltz, the simulated AHA did something similar at Screwllum's behest, thwarting Polka Kakamond's Knowable Domain, exerted through her power of probability manipulation that allows her to force order and predictability. AHA, by Elation, was also able to foil it.
Preservation
All the way back in Simulated Universe: Gold & Gears, specifically during Supreme Inorganic: Sanguine Condolences (III), we're told that Dongfang Qixing, the co-founder of the IPC, is capable of keeping things in control through omens--believed to be the visions or whispers of Terminus.
The means by which Terminus is likely traced can be discovered in the IPC Cuckoo Clock and the Broken Cuckoo Clock, which visually appear to be the same cuckoo clock. What both seem to imply is that this is the means by which the IPC tracked and possibly gathered divinations from Terminus, implying that the blessings of Finality alone aren't needed to achieve this. As this was done through Preservation.
The Hunt
During The Discreet Charm of a Streamer Girl, No AHA at Full Moon, Yaoguang confides in Sunday what would've happened if she would've donned the Supplicant's Mask: she would've become a "Nous" through the power of the Hunt, of the unique Spiritus she boasts, and locked in Planarcadia's doom. In doing so, it would've spelled unavoidable disaster.
Erudition
In the Simulated Universe: Unknowable Domain, Genius & Prophecy (II), the Erudition's "version" of the Solitary Waves Theory is the Circle of Knowledge. Within it, it governs what is knowable and what is unknown; in surpassing it in some way, new variables are introduced into the state of the cosmos via the new knowledge gained that can potentially lead to Finality if it becomes too chaotic, matching the Theory's difference between predetermined orderliness or chaotic disaster.
In Fu Xuan's relevant voicelines, she also ponders how gazing into the future in a manner matching the Erudition/Nous has the potential to lock in certain fates. Given how the Matrix was canonly inspired by Nous, it stands to reason that this also counts as Erudition.
Remembrance
Another prominent example was in the Myriad Celestia, Exotale: Scene 8, one of the possibilities was that Cyrene would utilize the power of Remembrance to freeze the universe before Irontomb could actualize and destroy it, completely stopping the flow of time so that it would remain frozen until the end of time.
In becoming the 4th Path that could've led the universe to Finality, this is another example of a Path altering the destiny of the cosmos.
Elio controlling the Script?
As noted in Cat Among Pigeons, The Devil in Velvet, Elio doesn't seem to actively control the script/fate so much as divine the future's many branches and choose pathways for the Stellaron Hunters (and Nameless) to follow for the best outcome. We see this detailed in the "bad endings" where Elio is credited as a Script Supervisor/Screenplay Director, and again in Exotale: Scene 8 that showed us a bad ending for Amphoreus he foresaw wherein Remembrance could've become the 4th Path in the Theory of the Four Apocalypses, a doomsday vision that informs much of HSR's current trajectory.
In The Generative Grammar of Liquid Modernity, So Laughed the Masses, the script being a be all, end all is completely debunked. Simply put, while Elio is an undoubtedly prolific seer, it completely nullifies the idea that he's capable of controlling anyone--let alone the Stellaron Hunters--through his scripts. What they are is a road map to achieve the best possible outcome for a given circumstance, not a locked destiny that controls the people it involves against their will.
Conclusion
To summarize, it's not impossible for Pathstriders of other Paths to potentially interfere with the predictions of Finality/Terminus, or for seers like Elio/the Omen Vanguards to be foiled simply because Terminus isn't the only way to see the future via Finality, as we've seen with Yaoguang and the Eye of Istvara or the IPC and their cuckoo clocks; let alone control destiny itself. Nevermind the fact that other modes can reliably foresee aspects of the future (such as Erudition (Nous) or through diviners of the other Paths (ex. Fu Xuan and her Omniscia (gifted by Nous)).
While seers like Elio are undeniably gifted, their foresight isn't absolute and, because of the Solitary Waves Theory, any Path has the potential to alter the fate of the cosmos at any time.