she wants to know if it's feasible to apply for another 6 month
extension while the current one is still pending.
Yes, she can apply for another extension of stay while the current one is still pending. There is no limit to the number of consecutive extensions of stays that can be granted.
If the first extension of stay is approved, then she can continue to stay while the second extension of stay is pending since the second extension of stay was filed during the period of stay granted when the first extension of stay was approved. If the first extension of stay is denied, she will still have to leave immediately.
would it be possible to apply for green cards for them, without them
having to go back to their home country, if she sponsors them?
Yes, if your sister-in-law is a US citizen and is at least 21, she can petition her parents to immigrate and they can do Adjustment of Status in the US. They would file the I-130 petition and I-485 Adjustment of Status together (each of those requires many additional forms and documents) for each parent. Parents of US citizens are in the Immediate Relative category and do not need to be in status to do Adjustment of Status. However, they cannot leave the US while their I-485 is pending unless they are granted Advance Parole before leaving, or they will automatically abandon their I-485.
Also, if they plan to apply for Adjustment of Status, they should not apply for extension of stay.