The limit is when the organization reforms or collapses.
I join you in your cynicism and am the kind of person to think that there are few allies and primarily mutual interests. If interests align, then you can have a functional team. If not, you get the sum of the winners according to the incentives management set.
Many companies structure incentives so that much of the time, it is in the interests of an individual to sabotage and chase credit simply because management is focused on certain things to the exclusion of others or tends to blame certain types of problems on certain classes of employees, i.e. a bad API gets blamed on developers even if the requirements were wrong.
These types of incentives are surprisingly common. Are there a finite number of promotions available? Is there a hard cap on departmental raises for the year, with them distributed according to some performance formula? Does the company stack rank? Has the team lead just left and more than one person wants the job?
Congrats! You have made a competitive environment. Finite rewards create scarcity. Scarcity creates competition. It doesn't matter how much some higher up might praise collaboration and cooperation if they are fundamentally rewarding based on individual performance and are evaluating individual performance according to a relative rather than an absolute standard.
So what can you do? Mutual interests can provide for (temporary) alliances.
I had one school project where a portion of the grade was based on peer assessments of you and people who were deemed to have a larger contribution on the basis of these assessments got higher grades. If someone was deemed to be an underperformer from these reports, their grade could be reduced and transferred to you.
What ended up happening is that some people wrote their reviews together to criticize the other team members for the same behaviors (and with the same anecdotes) while making sure to have consistent stories when praising each other. They got 5% extra for themselves while knocking 5% off their teammates.
I once had to deal with a presenting team member who repeatedly clicked through my part of presentations as my ideas competed with his and handed the clicker to someone else. My solution was to prime the room by giving the presentation beforehand to people who I thought agreed with me and giving them the arguments to shoot down his part either as he was giving it or during question phase. It seemed like his ideas were being casually dismantled and were poorly thought out. That gave me the space to interject and say "well, consider this idea instead." I got to seem more capable amongst the presenting members. The people got to score hits on a proposal they did not like early in the discussion, pre-emptively weakening it.
In the case of an internal pitch competition, a friend had a project which she realized was a boondoggle well into it. Problem is, winning it usually helped a person get a full-time job. She redesigned the project to give prominent roles and high praise to all the senior managers, who were also the judges and she won.
Now, most of these alliances are not going to be terribly productive for the class/project/company except indirectly.
Others will be allies when there are shared interests and you are not competing for the same thing.
Figure out who will benefit from advancing a goal you want to achieve, but will not be disadvantaged by your success if you succeed. Those are the people who might be willing to work with you.