I run two screens on an old I5 computer with no issues. So I'd suspect that three would not be a problem at all. Unless the software you are using is super fussy. Check the specs of the software and system requirements. Given that you also want touch screen capability, I'd be checking the system requirements of the screens, too.
I'm no expert in this field so, please wait for someone here who may be more knowledgeable of you specific needs.
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