His killers seemed to think he was trying to be a king but what did Caesar think he was doing? What did he say he wanted? Was Shakespeare Brutus right in saying that Caesar was ambitions and that was it? He was just a run of the mill power grabber?
If I knew what Caesar thought he was doing, I would be published and in a tenured position in an Ivy league school.
We know his stated reasons for fighting the civil war: the senate abused the tribunes by chasing Curio and Antony out of Rome, and by ignoring the law of the 10 tribunes that allowed Caesar to stand for election in absentia.
There are two main interpretations: the cynical one, that has been mainstream for quite a while, is that these reasons are just fig leaves Caesar used to justify his power grab, i.e. he really wanted to be sole ruler of Rome and these complaints were just an excuse.
The more modern interpretation proposed by people like Morstein-Marx is that these complaints were honest. They both have to do with the senate disrespecting the tribunes, who were the people's representatives. In Roman tradition, during the Conflict of the Orders, the senate and the people were at odds over a number of things, and getting elected quasi-magistrates to protect the people from abuses of the senate and magistrates was a major concession that allowed coexistence of the senate and the people. And while the tribunes chased out of the senate were Caesar's allies, and the law of the Ten Tribunes allowed Caesar to stand for election in absentia, it's not as self-serving as it seems. In effect, the senate has broken the ancient deal with the people by ignoring the tribunes, and Caesar saw it as a real constitutional crisis. This is my interpretation.
After the civil war, Caesar started on a number of public works projects that had been neglected for ages. The curia had burned down in 52, and had never been rebuilt, and the forum was too small to accommodate both the political and economic activity. He also famously reworked the calendar to a solar 365 day calendar. He started a state library. He increased the number of magistrates for smoother administration of the state (Rome traditionally had a shockingly low number of magistrates), and he increased the size of the senate, which allowed for smoother operation of the courts.
You could say things like, since the new forum has a planned temple to Venus, and the new senators and new magistrates would be indebted to him, this was all about self aggrandizement, but it's also clear that they were necessary administrative changes for the smooth operation of the government.
Now, after the assassination, Antony and the assassins negotiated about the future of the state, and they agreed to confirm all of Caesar's official acts, including his political appointments, so it's clear that Caesar's policies were not at issue. Brutus and Cassius wanted their appointments to Greece and Syria. Decimus Brutus wanted his position in Gaul.
So what did Caesar do that upset the assassins? Well, one thing that comes up, I think in Plutarch, was that he was seated while overseeing construction of his forum when a delegation of senators approached him, and he didn't stand to greet them. That could have been an intentional insult, or it could be he was sick or distracted. Expanding the senate and the magistracies reduced competition for those positions and so might seem to have reduced the social standing of the people who previously held those positions, and bringing in new senators from the provinces might have been seen as an especial insult, but again, all these things were ratified after the assassination so it doesn't seem like those were issues per se.
Then there's holding repeated consulships and the dictatorships. Caesar was dictator in 48, but both consuls were in Greece with Pompey and so someone needed to hold elections, and dictator had been used for that before, and he dropped it after 11 days and used the office of consul for the rest of the year. Late in 48 he was appointed dictator for one year, He was consul for 46-45. He was dictator for ten years after the battle of Thapsus. And then the crown incident at the lupercalia, and dictator for life.
Again, you could argue all these offices were self-aggrandizement, or they were necessary for restructuring the state in an ordered way. That's my best guess about what the assassins were up to, but it doesn't help with Caesar's intentions much.
So sorry "I don't know" is the only answer I have. No one really knows. This is the best I can do.
I think just as important a question to ask as what Caesar thought he was doing is what the assassins thought they were doing. Meyer, in his biography of Caesar, quotes an unnamed scholar as saying something like "the assassination wasn't only a sin; it was a mistake" a position Meyer rejects,