How many nested stable (1 Mio years) orbits are theoretically possible?
Yes, it's possible to have many nested levels, all stable. Each nested orbit needs to be inside the Hill sphere of its central body in order to be stable.

You can't nest any further when the Hill sphere gets too close to the Roche limit. Below the Roche limit the satellite disintegrates.

The exact number of nested levels depends very greatly on the characteristics of all bodies involved.