It takes two or three flushes to clear the toilet bowl

[Terry]

When it takes several flushes, the first thing I check for, is the fill tube between the fill valve, and the overflow tube.
It should be pointing down the overflow tube. This is what fills the bowl after the flush.
If the bowl is not filled prior to flushing, the first flush from the tank, merely fills the bowl, getting it ready for the next try.

The second cause, is normally an object in the trapway of the bowl that is slowing the siphon action of the flush.
This can be a toothbrush, pen, small toys, soap, or bottles.
Removing objects from the trapway will restore the suction needed for the siphon.
I sometimes use a “closet auger” with a fairly large end, about 1-3/8” in diameter.
The smaller augers or snakes will sometimes bypass the object and not move them out.
In some cases, I need to remove the bowl, looking into the exit of the bowl, and see what is there, sometimes running the auger in from the bottom, and pushing the object out the top of the bowl.
A trapway with tight bends, may have a lodged object at the top of the bend.
It’s pretty easy to get a pencil stuck there. A small mirror may help to locate it.
If you can’t remove objects, and sometimes you can’t, then replacing the bowl may be the only cure.

The third cause, would be plugged rim holes under the bowl lip.
If these have become plugged, then a wire coat hanger can unplug them.

The fourth cause, would be a main line backup. If that is the case, you might notice water seeping out from under the bowl.
That means the line is full, and flushing the toilet, the water really has no place to go.
A shower or tub on the same floor may show signs of backing up too.

[hj]

You forgot the fifth possibility, although it is somewhat rare, and that is something that went down the flush valve and is caught in the toilet's waterway. I had one a few months ago, where the water would not even leave the bowl. After trying many ways to unplug it, I replaced the toilet and broke the bowl. There was a blue jelly caught at the point where the water would go down to the jet and the rest of it to the rim. It was in a swimming pool supply store so I looked around to see what it could have been, and found a container of blue stuff that was for use in the pool, but was not sure if it was the actual material. Another time, I had a customer with many of the old Crane toilets with the ceramic seat and the hinged flapper with a Styrofoam float on the bottom. I discovered that the tanks had been assembled to the bowls without using the plastic "stiffener",(which had a plastic "cross hair" inside it and fit inside the tank to bowl gasket). The rubber would deteriorate the float would drop off, and since the cross hair was not there to catch it, it dropped into the bowl, obstructing the flow to the jet. I would fish them out with a stick of silfos heated so it melted into the plastic and then hardened. I once removed FOUR of them from one bowl. Back in the fifties, when Kohler was on strike, some union members hired on as scabs to sabotage the products. I would receive toilets that would not flush, and when the tanks were removed, there were paper towels pushed into the rim flush passages.