Yes, but it could keep the records needed to do it.
That said, I very much doubt that there is an off the shelf plugin that does this and meets all the regulatory requirements (which I am assuming the OP has researched). On the other hand, I assume the developer who did the backend can develop this too.
Having worked in a City financial regulation firm, this is an incredibly difficult thing to do in English law; this is not something that unfortunately can casually be addressed by a wordpress plugin. Any such solution would require probably about 10-20k in legal fees, which would dwarf the cost of getting the plug in developed!