Is it possible to open a specific form to create a new record when the + is clicked in a lookup field?

As the title says, I want to direct users to a very specific Contact form whenever they attempt to add a new a record from the + (new) button on a lookup field.

The reason for this is to create the record with specific data elements set (via JS or a business rule) that I don't want to rely on the end-user to get right.

I'm open to any manner of suggestion for accomplishing this; C# plugin, JavaScript, etc.