The Financial Conduct Authority (FCA) is looking at ways to bolster the provisions in the Senior Managers' and Certification Regime, which has applied to the banking sector from 7 March.
Consultations launched include one on requiring overseas banks to tell UK branch staff about the whistleblowing services the regulators offer and one on extending various rules to non-executive directors.
The FCA also published a discussion paper on how heads of legal departments in firms affected by the rules should be treated.
"Generally, we have observed that firms are taking their responsibilities seriously and have broadly got the regime right," said Andrew Bailey, chief executive of the FCA. "But we recognise culture change takes time and there is still more to do. So we have to keep a watchful eye on the progress firms are making."
Jonathan Rogers, head of financial services regulatory at Taylor Wessing, remarked: "Andrew Bailey's positive tone is interesting and welcome given that the Senior Managers and Certification Regime will be rolled out across all financial services firms in 2018. It is a credit to the sector that the FCA feels that there has been a sincere level of commitment to cultural change on a pervasive basis throughout firms."
Adrian Crawford, Kingsley Napley employment partner, added: "The changes for overseas banks with branches in the UK make perfect sense, as does including NEDs within the existing conduct rules. The treatment of heads of legal is an issue which has been under discussion for some time."
However, the Law Society warned including legal functions in the regime could "create conflict".
Law Society chief executive Catherine Dixon added: "We welcome the opportunity to discuss our concerns with the FCA during their consultation."