The “human capabilities” approach can be thought of as a moral theory that straddles the divide between libertarian and utilitarian theories. Libertarianism focuses on formal freedoms, i.e., negative rights. Utilitarianism focuses on what actually happens. The human capabilities approach focuses on whether people have the opportunities to fulfil their human potential. This goes further than libertarianism (which just focuses on the absence of obstacles posed by others) but stops short of utilitarianism, because of its focus is on capabilities, not outcomes.
This approach, in various forms, has been developed by Amartya Sen and by Martha Nussbaum.
A case for open borders can be made using the human capabilities model. To some extent, this would simply be a combination of the libertarian case and the utilitarian case. If you have a more egalitarian perspective of human capabilities, it can also borrow from the egalitarian case.
Writings that make the case for (more) open borders based on the human capabilities approach
- Immigration, Ethics, and the Capability Approach (available here) by Mathias Risse, Human Development Research Paper 2009/34.
- Open Borders Allow People, Not Their Place of Birth, To Control Their Lives by Joel Newman, March 31, 2014, Open Borders: The Case.
What is the human capabilities approach?
The Wikipedia page on the subject is here. The references in the page offer a good starting point for reading about this approach.
There is also a website on the capability approach here.