Has there been much research on the Iwasawa theory of bi-quadratic fields?

The simplest non-trivial example of $$\mathbb{Z}_p$$-extensions happen over imaginary quadratic fields and I've seen a good amount of research done here (from my understanding still a lot to learn). I would think that the next step up in complexity would be looking at the $$\mathbb{Z}_p$$-extensions of bi-quadratic fields, say $$k = \mathbb{Q}(\sqrt{-m}, \sqrt{n})$$ where $$m \in \mathbb{Z}^+, n \in \mathbb{Z}$$ are square free. I've been searching around but can't seem to find any work done in this area. In particular, I'm interested in Iwasawa's $$\lambda$$-invariant for the cyclotomic $$\mathbb{Z}_p$$-extension over $$k$$. Does anyone know of any papers or research that have to do with this? Thanks for any help.

Edit: After a bit of thought I realized that this may not be so interesting. I think that we can determine $$\lambda^-$$ (the minus part of Iwasawa's lambda invariant for the cyclotomic $$\mathbb{Z}_p$$ extension) from the $$\lambda$$-invariants of the two imaginary subfields of $$k$$. That is, $$\lambda^- = \lambda_{\chi_1} + \lambda_{\chi_2}$$, where $$\chi_1, \chi_2$$ are the odd characters belonging the imaginary quadratic subfields. We have $$\lambda = \lambda^- + \lambda^+$$, but $$\lambda^+$$ is expected to be 0 by Vandiver's conjecture.