Can we get an extension on our visa in Thailand if we have a flight booked home, but are still short on days?

Never overstay if at all possible

It’s never a good plan to intentionally overstay. Go to Laos for a few days and re-enter, so you get another 60 days visa free (assuming that is what you qualify for).

Change your tickets.

Some offices give you an extension denied stamp, giving you 7 days. This is not an extension however, and that matters for how it's counted: the 7 days start counting from the day you apply. So best case scenario, applying on the very last day, you get only 6 extra days. Looking also at weekend closures, you can only makes this work if you apply on Friday 29 November.

You can also go for a border bounce to refresh the initial 60 days, taking the freedom to assume that you made two mistakes in your story and that you are not on any visa and also not for 90 days, but on 60 days visa exempt. Then you save yourself also the first (and only) extension. Just keep in mind that entering Laos or Cambodia costs money as well so from a cost perspective the two solutions may come out similar still.

You can go lao and come back in again to get another 60 days if you are on visa exempted ?

You would only get a 30 day extension from a visa exempt entry.

Some offices will allow you to apply for a second time but you will be denied the extension and given 7 days to leave the country. This denial costs the same as your original extension.