(edit; in addition the psd2 legislatiob, and specifically the technical guidance, does touch on concepts like 4th party, relaying parties and technical partners - so the exoectation of the regulator is that this will emerge)
* your bank is an "ASPSP"
* the second party is you
* the company (third party) is the AISP
"For businesses that only carry on account information services, there is an option to become a ‘registered account information service provider’. These providers have no capital requirements and need to meet fewer conditions than authorised firms. Businesses that provide payment initiation services must be authorised and must have a minimum of €50,000 in initial capital (or higher if they provide certain other payment services). Both AISPs and PISPs have to hold professional indemnity insurance (PII). The EBA has developed Guidelines on PII (link is external)."
Correct? This doesn't specifically rule out being a relay, but I guess there is more detail/restrictions in another document.
See also: https://www.out-law.com/en/articles/2017/june/fca-urged-to-a...