Kettle logic
Kettle logic is when you give several different, contradictory reasons for the same thing—like the person who said he never borrowed the kettle, it was already broken when he got it, and he returned it in perfect condition. The reasons can't all be true, so your case falls apart. The fallacy is to offer multiple defences that undermine each other. The remedy is to give one consistent story or to acknowledge the tension.
Examples
I didn't take it; and if I did, I gave it back; and anyway it was already broken.
I wasn't there. And if I was, I didn't see anything. And if I did, it wasn't like that.
The project was on time. And if it wasn't, the client changed the scope. And we were under budget anyway.
I never said that. And if I did, I was joking. And anyway it's true.
We didn't promise that. And if we did, we met it. And the contract allows it.