You can certainly open multiple 529 accounts in different states and withdraw from the accounts simultaneously, but the $10,000/year limit for K-12 tuition is per beneficiary, not per 529 account. So you could withdraw $2,000 from each of five accounts every year, but you would still be limited to spending a maximum of $10,000 total each year from 529 accounts for K-12 tuition for the same beneficiary.