When it comes to expressing one's involvement in something, the phrase "have a hand in" comes to mind. However, there are several other synonyms that can be used to convey the same meaning. These include playing a part in, having a role in, contributing to, participating in, being a factor in, being involved in, and having a say in. Each of these phrases can be used interchangeably with "have a hand in" and all convey a sense of shared responsibility or cooperation with others. It's important to have a variety of vocabulary at your disposal to ensure clear and effective communication.