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.