Yes, it is possible, and may not be uncommon. Perhaps one of the most well studied cases is the tumor suppressor p53 (transcription factor), which induces MDM2 (its transcriptional target) and, in turn the MDM2 protein interacts and degrades p53. This feedback loop leads to the p53 oscillator. The following book chapter by Gahit Lahav is a good way to start (http://lahav.med.harvard.edu/publications/Lahav%20Adv%20Exp%20Med%20Biol.pdf).

Good luck,

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