During music theory class I was taught in C major we have six possible secondary dominant chords that resolve to non-tonic diatonic chords:
A7 (- Dm)
B7 (- Em)
C7 (- F)
D7 (- G)
E7 (- Am)
F#7 (- Bdim)
They are V7/ii, V7/iii, V7/IV, V7/V, V7/vi, and V7/vii°, respectively.
Can secondary dominants be used to resolve to non-diatonic chords as well?
It's not entirely clear to me what the question is about, but here's a guess. And because comments can't have pictures in them. Here's a snippet from "Kun joulu on", a classic Finnish Christmas song composed by Otto Kotilainen, lyrics by Alpo Noponen.
This is from some random arrangement, but the relevant part is there. The song is in Em, and starting from measure 14 there's a chain of secondary dominants C#7 - F#7 - B7 - Em. The first C#7 is "V of V of V", then F#7 is "V of V", and finally B7 is the real V of I chord going into tonic Em. This happens so rapidly that IMO the tonic stays in Em very strongly the whole time, so there's no modulation.
In my opinion, the things they teach you on basic theory such as "dominant" and "secondary dominant" is some kind of harmony for dummies, stereotypical examples that you can easily classify as being this or that. But in reality, you'll encounter all sorts of halfway-in-between hybrid behaviour that can be looked at from different perspectives, and many explanations can be justified at the same time.
The topic line talks about "tonicization" - which should usually change the definition of what is called "diatonic". So if that's really the point, then this answer doesn't really apply.
Secondary dominants often refer to a dominant built on the non I, IV, or V chord (some writers call these secondary chords.) These chords resolve as though they were a normal dominant (and vii0 chords can do the same.)
However, there are two (obvious?) extra possibilities. First, a simple deceptive resolution is possible (G7 can resolve to A minor, V7-vi or even V7-VI which is common in minor keys). And second, a chromatic major (or seventh or similar) may resolve as a dominant. For example, E7 in (in C) would be expected to resolve to A-minor but A-major is possible. Likewise, a sudden chromatic chord, like Ab7 in the key of C major, could resolve to Db or Db minor. If not confirmed by both length and other chords (a quick return to the home key), these do not effect a modulation.
As an aside, Schoenberg and others point out that to establish a modulation, one needs a chord that "neutralized" the characteristic note(s) in the main key. For example in modulating from C to G, one needs a chord (or several) containing an F# to "neutralize" the F which is diatonic to C.
