A status quo in which all the gods are busy keeping each other in check seems like a great asset for a clever DIP or INT character, because there's always someone you can turn to who is already opposed to whoever is trying to get you to do things.
Up to a point.
On the other hand, a status quo in which all the gods are busy keeping each other in check and where you have a reputation for going behind God N's back to persuade God N+1 to meddle in God N's plans, potentially for multiple values of 'N...'
Again, see my remarks about how to live a long and peaceful life.
To borrow from
Game of Thrones, "Chaos is a ladder" sure seemed to be working well for Littlefinger... except the part where multiple times he had to flee as everything burned down around him, often for reasons he was complicit in, and where eventually he wound up dead.
Assuming you can actually contact said people.
Zeus isn't above putting Gods on house arrest.
Let's put it this way.
There are hypothetical scenarios where Zeus (or some other overwhelmingly
strong god) decides to try and coerce Polyhymnia (or some other overwhelmingly
persuasive god) to act as a proxy and makes it work.
However, most scenarios like this work best as what I've heard thought of as a "white room" scenario. No external uncontrolled variables, no complications, a straightforward test of power and will and absolute maximum effort against absolute maximum effort. It's easy to imagine the scenario working if we imagine Zeus being 100% resolute and determined to make it work at any cost. If Zeus takes elaborate precautions because he's convinced that this
must work and dedicates a lot of time and energy to making it work before even beginning to try. If Zeus somehow fortifies himself against any possibility of persuasion. If "there is no tomorrow" and he's not worrying about how his actions will shape his interactions with the people around him for the next thousand years.
But every deviation from the isolated white room scenario makes things muddier, more uncertain, less likely to end in "Zeus gets everything he wants." The white room looks less and less like the reality if one factors in that Zeus may not actually be 100% determined to do things and refuse to even talk about it. Or that Zeus probably
likes Polyhymnia because people who can beat a DC 50 Diplomacy check using charades are typically going to be seen as likeable by almost anyone they want. Or that living with the same people for centuries means, for better or for worse, finding some accommodation with them that isn't a constant pain and doesn't destabilize the situation and throw things into chaos every few decades. Et cetera, et cetera.
...
We may observe that a pantheon has been around for thousands of years and has somehow managed to avoid massively slaughtering each other in one round of civil war after another for at least the past few millennia. If this is the case, it seems likely that the pantheon would have reached some kind of equilibrium fairly early on, and that this equilibrium is fairly resilient to disturbances. Which suggests that the individuals within that pantheon will be quite reluctant to upset the applecart without a very good reason to think they
must do things in that specific way.