We did this for a couple of years with one of our kids. PE, art, music, computer, science labs (elementary), and some incidental academics (neither graded nor mandatory, just present) at school, all core academics at home in modalities and with curricula of our choice.
While in our case this was a private school, a number of public schools allow this for homeschoolers.
You might consider asking your school if this is an option. In my experience, privates tend to be more open to individualized solutions, especially if you are still paying tuition...
