Let’s start with the Earth-Moon system, but tweak it so that we can get the ‘most’ total solar eclipses possible. Obviously if we put the Moon into an orbit in the Earth’s orbital plane, we’d get a total solar eclipse somewhere between the Tropics every month. But can we do better?*
Can we stably put the Moon into a polar orbit such that we can sweep an eclipse from north to south or vice versa every month, instead? Maybe this gives us a greater swath of Earth from which an eclipse is visible. Bringing the Moon in as close as possible shortens the lunar month so we get eclipses more frequently, too. And polar tides would be kinda cool, right?
*Poorly specified, I know, but make of it what you will - in the plane of the ecliptic, a total eclipse won’t be seen north or south of the Tropics, so tilting it a little bit gets you total eclipses at higher latitudes but those are quicker. Maybe think of it as trying to minimize Earth’s total solar irradiation by blocking the Sun as much as possible.