Other possible positions for "se" ?

Hi, my question is regarding the quiz item:

Pedro is going to start thinking [and continue thinking] that we're silly.
Pedro se va a quedar pensando que somos dos tontas.

Are there other possibilities for the position of the "se" ?   In particular, I'm wondering about these:

Pedro va a quedarse pensando que somos dos tontas.
Pedro va a quedar pensándose que somos dos tontas.

If either of those is grammatically correct, is there any difference in meaning/tone/frequency of usage?

Thanks!