What is stopping everyone but a single guy in the party (most of the time the guy with the highest Influence will do the buying anyway) to burn all theirs for exceedingly rare items?

Could you cite the exact rule that you're referring to? The closest I could find was on pg. 269; " When attempting an Influence test, before rolling, an Acolyte may choose to decrease his Influence by 1d5 in order to automatically succeed. "

If that is what you are referring to, I can swiftly tell you that acquiring items is now called a Requisition Test (..why they changed it from Acquisitions Test is beyond me - could it simply be a copy-paste holdover from Only War, where you actually Requisitioned Items instead of Acquiring them in general?). It is not an Influence Test.

Could you cite the exact rule that you're referring to? The closest I could find was on pg. 269; " When attempting an Influence test, before rolling, an Acolyte may choose to decrease his Influence by 1d5 in order to automatically succeed. "

If that is what you are referring to, I can swiftly tell you that acquiring items is now called a Requisition Test (..why they changed it from Acquisitions Test is beyond me - could it simply be a copy-paste holdover from Only War, where you actually Requisitioned Items instead of Acquiring them in general?). It is not an Influence Test.

Does it explicitly say anywhere that the requisition test is distinct from an Influence test (an thus this rule does not apply)? Because Requisition is literally the first thing listed under the Uses of Influence section on page 268.

It's also really weird to me that this rule is buried in this section, which mostly contains information for the GM. A player could very easily have no idea they were allowed to do this given it's buried in a paragraph describing an example situation where players can lose influence.

What is stopping everyone but a single guy in the party (most of the time the guy with the highest Influence will do the buying anyway) to burn all theirs for exceedingly rare items?

First off, by my reading, you can't burn Influence to auto-succeed if you had a less than zero chance in the first place.

Let's assume a starting character with 35 Influence. He burns 1d5 Influence to get a suit of Light Power Armour and rolls a 2. He then burns another 1d5 Influence to get a Meltagun and rolls a 3. At this point he can no longer burn Influence to get Very Rare items, because the -30 modifer for Very Rare drops him down to 0. He could keep burning influence to get Rare Items until his Influence is 20, but I think few players would go further than that.

So let's say he's blinged himself out with Light Power Armour, a Meltagun with a Custom Grip and an Auxilliary Grenade Launcher, a Chameleonline cloak and an advanced med-kit, at the cost of (on average), 18 points of Influence. He's knocked his Influence down to 17 from it's starting position of 35. He's also dropped the group's Subtlety by a whopping 14 points. If everyone in the group does this, the group's Subtlety will be completely wiped out.

Yes, he's got some really powerful armour and a very killy gun. He'll probably go through mundane opposition like...well like a meltagun through mundane opposition. But he's also a) torpedoed any chance of a softly-softly approach, b) run up a line of credit with half a dozen Imperial agencies and c) he hasn't exactly walked away with Terminator Armour and a Grav Cannon, just the top shelf stuff from the local Guard and Sororitas armouries (yeah, if you've pulled all the strings you've got to get some human suitable power armour at zero notice, the armour probably does have boobs. Your male acolyte is gonna have to learn to like it or lump it).

Burning permanent influence is basicaly saying to some other Imperial organization "I will owe you a big favor for this". If you are a Inquisitorial acolyte and say that, yeah, the first couple of times, you can get some pretty potent ordnance in exhange. But you're trading off the ability to walk in a get lasgun ammo tommorow and the next day, week, month, year in exhange for a meltagun right now. Long term, if you keep and build that permanent influence, you can turn it into enough meltaguns to equip a whole squad of borrowed stormtroopers. Meltaguns can be stolen. Power armour can break. Influence is much harder to lose.

Now, the objection to this is that you only need one character to build up Influence long term, so why not have the other four splurge on whatever passes their fancy? Well, first off, one character can't be everywhere at once. You may need to requisition a Aquila Lander now, not when your Adept can get across town to the voidport. As GM, I'd be perfectly willing to say things like "You've got 6 hours in port between ships, that's enough time for each of you to make one Requisition test if you like" and if 4 of the characters have pissed their influence away, then only the Adept has a decent chance of getting anything with that one test.

Secondly, has your character just decided that permanent minionhood is what they want? If only one Acolyte is growing in fame and respect and cultivating ties to local power structures, then it's pretty clear which Acolyte might become an Interrogator one day, isn't it? I don't know about you, but I've had enough 40k RPG games turn PVPish that I'd like to have my own power and influence rather than depending on Adept Bob. Also, Adept Bob might catch a boltgun round one day and then who'll requisition my meltagun ammo?

Lastly, consider the in universe reality. Is your character the kind of person who'd be happy grabbing up a load of flashy equipment and the forever being "That Acolyte who owes us big time for that suit of power armour we lent him". Do you want every communication with every other Imperial organization to start "About that favor you owe us..."?

I'm glad the option exists, not least for players who might want to play a Sororitas or a Death Cult Assassin and are happy to trade a bit of Influence to be able to play with the iconic equipment of power-armour-and-a-bolter or twin-power-swords, but I think for most PCs, burning Influence for flashy gear is a bit of a sucker's choice.

And to add to it I say never forget about location modifiers and the Commerce roll, because if there ain't no meltaguns on the planet then no you can't beg, borrow, or steal it, and if you can't find someone who has one then you can't get one.

And as a an extra bonus; The way I personally run it in my games, which even my most greedy players agree is a fair way to do it, is that any item with a total modifier to the test that would be more than -60 in theory (i.e. -50 for Near unique, -30 for best quality but +0 for location and +10 for Commerce roll would be a -70 in theory even though the game only allows for a -60 total to tests) is impossible for that character to find, period the end I don't care what you do. Now I will note that this is total modifier, so after you include bonuses or penalties from the Commerce test, and location modifier, and things like Peer or the Administratum background bonus. So if you are supremely connected, a shrewd trader, and on a forge world that specializes in arcane weapons then sure you can find that best quality grav gun, but can you buy it? Which comes to the other thing I house rule on the subject, if the total negative for an item (before modification) is higher than your Influence then you cannot burn influence to Requisition it. So for example a grav gun is extremely rare (-40), best quality tacks on another (-30), so if you want to be able to buy it without having to Test by burning Influence then you have to have a 70 or higher influence, because I'm sorry but you need some SERIOUS clout to be able to get something that precious just by calling in favors, putting yourself in debt to a person, or even throwing around the "do you know who I serve" bit, people have to know and respect you a whole lot before they give up what is most likely an irreplaceable religious relic (because priests of Mars are weird) of such dire potency and rarity.

So that's my two cents, and how I try to keep the game balanced through what I see as simple and intuitive rules.

Bumping this archaic thread rather than make a new one since I found it on Google.

I just stumbled on this rule after making an effort to read the entire book to make sure nothing small was being missed by our group. As a GM the issue I have isn't really someone abusing it and getting totally blinged out. The issue I have is if one or two characters saying "I want a best crafted near unique item" spending 2-3 of their influence getting it and dropping 4 subtly. at the very beginning of an adventure This is not a big loss for them or something that would really result in tons of favors owed or incredible increase in suspicion just based on the numbers. Then I have a situation where some of the party is vastly overpowered and the other half isn't which causes fights to be incredibly wonky and also my designed encounters really under-powered requiring a lot of work to adjust on the fly. I've played a game where one player was given a Storm Hammer early on and it was incredibly un-fun to watch that person trivializing every encounter while the rest of us just picked off the leftovers.

I'm thinking that my personal house rule will be that if the test is impossible for the player to pass (not counting the 1 always succeeds rule) then you may not use this. It just sucks to have to house rule this sort of thing because it's so obviously destabilizing.

From the core rulebook, page 268:

"When attempting an Influence test, before rolling, an Acolyte may choose to decrease his Influence by 1d5 in order to automatically succeed. If degrees of success are important, the Acolyte is considered to have achieved a number equal to his Fellowship bonus. Note that in situations where no test is possible, this use of Influence cannot be made: the situation is beyond even the Acolyte’s ability, or the item is impossible to acquire. "

That makes it very difficult to acquire really game-breaking items early in the game.