Unlikely that it will work perfectly, but someone might do just what you suggest in limited cases. You're not just asking for two diverse chemical classes, you're also looking at diverse sample types. The traces of plasticizer compounds in animal tissue is too complex a sample -- given the interference from the tissues. Generally, you'll want to digest it free, and analyze by GC, but then you're limited in the variety of reagents you can test for.
Similarly, particles of plastics can be analyzed on an FTIR with an ATR crystal with ease, but the traces of plasticizers would end up lost in the noise.
That's not to say that if someone wanted to know just one, they wouldn't try using the "incorrect" instrument, its just that any method they develop would be highly;y restricted in what they can detect.
By the by, why would you want to limit yourself to just one type of instrument? Are you outfitting your own lab, or are you trying to write a script for a CSI-type story, wherein one instrument does very diverse tasks, in seconds, to perfect accuracy. Preferably manned by a woman wearing impeccable designer clothes better suited for a night clubbing than for working in a lab?