How can I get my iPhone 14 to ring more times before it rolls over to voicemail?

Contact your carrier to find out what options they might have in this regard.

Most carriers have a user support site that allows their customers to log on and choose some basic options with their service.

For example......AT&T allows their customers to choose the number rings between 1-6 before the incoming call will go to voicemail.

I don't think you can increase the number of rings.

Please contact your Carrier as VoiceMail is a carrier-specific feature --> Check your voicemail on iPhone - Apple Support

VoiceMail, whether it's visual voicemail or the traditional voicemail service, is a carrier-specific feature that depends on your cellular service provider. If you are experiencing any issues related to voicemail on your iPhone, it's essential to get in touch with your carrier for assistance.