Yes, adding custom fields is very possible but does require a dev to do so. If you know PHP you can see these extensions for Connections that add custom fields and use them for reference to add your own:
As additional reference, there is this blog post that walks thru adding them:
And lastly there is this demo plugin that show all the supported field types that can be added:
If you do not know PHP or have your own developer, I do provide custom development services. If you would like a quote, please contact me using the Contact link at the bottom of the page.
Hope that helps!