General:
* Include
* Comprise
* Encompass
* Embrace
* Contain
* Entail
* Implicate
* Engage
* Concern
* Affect
For participation:
* Participate
* Take part in
* Be part of
* Contribute to
For causing something:
* Cause
* Lead to
* Result in
* Contribute to
* Bring about
For connection:
* Connect
* Relate to
* Associate with
* Link to
For complexity:
* Complicate
* Entangle
The best synonym will depend on the specific meaning you want to convey. For example, if you're talking about a task that requires a lot of steps, "entail" might be a good choice. If you're talking about a person who is connected to a crime, "implicate" might be a better option.