There's no rule saying a spirit dog can't cast basketball

[Gol Golarion]

Hey, question to you folks to gauge how I should rule something. So, let's pretend for a minute that one of your players has decided to play a medium, and they're rolling with the archmage spirit. They accrue a fifth point of influence and hand over their character sheet to you, the GM.

Spirit (Su) wrote:

If a spirit ever attains 5 or more points of influence over the medium, the medium completely loses control to the spirit. He effectively becomes an NPC under the GM’s control until after he awakens the next day with the spirit gone.

Now, the archmage, perhaps being influenced by the party's face via NPC diplomacy and RP, decides to tag along in exchange for some time to stretch their legs and flex their magical muscles in the living world for a while. The archmage doesn't get a new character sheet, instead using the medium's skillset. Among their various tools is an ability that lets them gain influence in exchange for not consuming spell slots: Arcane Surge.

Arcane Surge (Su) wrote:

You can allow the archmage spirit to gain 1 point of inf luence over you in order to cast one of your medium spells known without expending a spell slot. When you do so, the caster level and DC of the spell increase by 1, and you can’t apply metamagic to the spell.

For the medium, this is a clearly limited resource - if they ever hit that 5th point, they get NPC'ified. But for the archmage, this doesn't actually seem to matter at all. There's no upper limit to the amount of influence they accrue, and there are no further downsides past 5. Would you, as the GM, be within the rules to just... cast all of the medium's spells with arcane surge every round forever, only ever touching your medium's spell slots for Wild Arcana to pull wizard spells they didn't prepare? Surely you could raise the drama by being a rogue powerhouse, but am I missing something? Does this work like i'm thinking?

[Pizza Lord]

A GM could do it if it's cool or awesome or to save the plot because the medium's player is now an NPC. In practicality, as a GM I wouldn't do this as a regular outcome, only as an 'it seems the most likely thing to be done in this situation' outcome, and then the spirit goes and does its own thing for 24 hours.

As for a bard influencing them. They'd have to really be able to perceive or know the spirit was in control, and most spirits are dead and very powerful, especially an archmage's spirit. It's possible that a logical, passionate, or very skilled persuasion might allow some direction, but likely they'd just pursue some archmage stuff, like researching or conducting tests by casting all the mediums (now unexpendable) spell on nearby targets to test out their effects, and the rest of the party is probably the closest guinea pigs.

The premise is that the medium is taking an action to allow greater influence over them. There comes a point where a spirit already has total influence over you or you have not more 'influence points' to give. While it's possible for some character to claim they're such a submissive or weak person they submit willingly to such spirits' influence (or claim it's just their personal outlook), in general a controlling force can't force you to submit further.

For instance, even domination effects which allow full control typically also state that the subject is struggling or battling for their own will (just losing). As such, a dominator can't just force someone to forgo or accept or willingly fail a will save over and over to keep control. Side note: in the case of charm effects, the charmer could persuade a person more easily to do so, because they're viewed as a trusted friend or could convince them they're casting a different spell, this isn't forcing, just tricking.

In this case, I don't think it's intended for a medium to ever want to lose control to a spirit (since they will likely have their own desires and drives and not care what happens to the medium). I suppose from an archmage spirit's outlook, someone might say, "Sure, they'd go around casting medium spells without expending slots just from mental curiosity to see what it's like" Sure, maybe once... or twice in a thousand years. They've probably already done it and, as and archmage, they probably know most medium spells and have cast them already. The spirit would more likely just go to a library, start reading a book, or delve into some great secret. Otherwise, with full control, the GM could just say it summons a great devil or demon and sacrifices or gives the medium's body to it in exchange for great knowledge and power or something.

A GM could do it... but it's probably not the intended penalty for reaching 5 influence unless he makes it part of the plot; like in 24 hours the medium 'awakens' in Hell or the Abyss or being forced to complete a task or something.

So yes, a GM could do something like that if they wanted, or to save the party, but it will likely result in some great downside to the medium's character beyond any other stuff (like taking a ton of damage, since the spirit doesn't care, getting scarred or mangled, or expending all their magic item charges or drinking their potions or using their scrolls or equipment); it's like being in a disposable NPCs character sheet and gear. "What does this potion do when I drink it, I wonder!", "I always wanted to know what cyanide tasted like! Now I can find out!"

A spirit could stand around and cast a bunch of free spells to help the party, but if in combat, just have it attacked or taking actions that don't care about the medium's body, like running past enemies and provoking AoO, just to test out a spell. At best, if the party were just sitting around, sure, the spirit could cast a bunch of the medium's buff spells at +1 power and without losing them... but it's still mostly spells the medium has (granted, could cast more of them, like bull's strength or something. And that doesn't mean the spirit then goes into combat with them or continues their mission or adventure for the rest of the day. It's just a friendly NPC caster at best... and the medium's player sitting out the next 24 hours.

[Trokarr]

So here’s a potentially broken exploit you could try. Get yourself a familiar that will have full progression with you (the Wasp Feat will get you one for the cost of a feat. The Familiar Bond route can get u one for 2 feats and a trait or go Eldritch Heritage:Arcane plus Boon Companion for 3 feats or u could go VMC Witch or Wizard but that’s 5 feats but u get the extra goodies from VMC too) Anyways give it the Parasite archetype and implant the thing in YOURSELF! At level 7 it can cast Dominate Person on you daily using your casting stats. You can choose to fail the save and let it gain control. If it doesn’t give you any orders you should act normally until it does. If you then let the Archmage gain total influence on you your Familiar can then Puppeteer the Archmage. You’ll probably need to have a pretty high DC to prevent the Archmage via your will save from making the save. If your familiar is successful then it will be in control of your body with all the Archmage powers. You still will wind up being an NPC for the day but at least you’ll be controlled by a familiar that (hopefully) has your best interests at heart instead of some Rando Archmage with their own inscrutable agendas. Don’t quote me on the 100% legality of this but you could see what ur GM thinks ;)

[Azothath]

reading the entry is helpful,
Medium's Spirits where the Influence Penalty is laid out.

With spirits I think GMs should have a personality and goal in mind for each type of spirit the medium picks up/discovers. That way he can roleplay the spirit as needed. This would act as authorial advice, foreshadowing, to intervention. You'd have to be in dire story straits to use intervention.