Jean Muggli Strahan claims in legal docs ... the former NFL superstar's on the hook for some big-time equestrian expenses for their twin teenage daughters -- Sophia and Isabella -- along with owing hundreds of thousands in back child support.

Jean says a huge chunk of what Strahan owes her is to cover their daughters' horseback riding bills ... which she claims amount to $450,802 since 2017. According to the docs, Michael agreed to go halfsies with Jean but hasn't paid up ... so she's seeking more than $225k from him.

In docs he filed, Michael says he never agreed to such an arrangement.

On top of that, Jean claims Michael has underpaid child support since 2010 ... because the monthly amount he pays hasn't been adjusted for cost of living. The docs say she wants $321,654 in back support to make it right.

In his filing, Michael admits part of their agreement does call for cost-of-living adjustments -- but adds, the language about how to come up with that number is "vague and indefinite." Translation: We need to agree on a formula to come up with the correct number.

That being said, by Jean's current calculation ... she's looking to get more than $547k.

We broke the story ... the exes were in a Manhattan court last month to face off over their previous settlement.

Michael and Jean married in 1999 but split in 2006, and the judge eventually awarded Jean $15.3 million in their divorce and ordered him to pay $18k/month in child support.

However, that amount was decreased to just under $13k a month in 2009 ... according to the docs.

Jean claims his monthly income is way more now than it was in '09, due to his gigs on "FOX NFL Sunday" and "Good Morning America," among other projects ... so he can afford to increase his child support again. She wants him to pay $18,378 a month going forward.