Multiple Double slit experiment

A double slit is usually in a first approximation (which you are dealing with in school, probably) just a pair of point sources which are a distance $d$ apart. Sure, each of the slits has technically a width $w$, but unless you are looking at double-slit diffraction and not the simpler$^1$ double-slit interference, you don't care about the size of the individual slits.

Now, the Huygens-Fresnel principle states that in the double-slit experiment, both slits act as point sources emitting spherical waves which will interfere everywhere on the other side on the slit screen. The detection screen is just there to allow for a simple geometric calculation of the pattern along that particular screen.

If you put a second slit screen behind the first one, possibly angled at an angle, no matter what kind of interference pattern might show up along that second slit-screen, the slits will still be pointlike and the secondary (and all subsequent after that) interference pattern will be more or less the same as the first one, barring intensity losses.

So in the first order approximation used in school and introductory optics classes, the interference pattern will not look any different.

Now, of course, if you extend your calculations to account for the diffraction each of the slits composing the double slit, their width $w$ comes into play and since the Huygens-Fresnel principle still says that each point in the slit emits a spherical wave, you will have to take into account the intensity variations the first screen will cause on subsequent ones.

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$^1$ Interference and diffraction are more or less the same thing in the sense that both are well explained with the Huygens-Fresnel principle. Usually in school, one deals only with double-slit interference, but you can of course ask what happens to the single-slit properties of each of the slits and how they effect the overall interference picture. That runs under the name of double-slit diffraction, see e.g. in these great MIT notes