I have 3 solutions and solution A requires built versions of the dlls from solution B and C in order to compile. it is not possible to merge it to one solution...
So far
According to this answer, I would recommend you to create your own batch file which will build the relevant solutions for you.
That's very handy to use because the build process will output the build progression (Similar to Output window in Visual Studio) to the command promote for each and every build executes.
Furthermore, in a case that you need to build one solution before the other, you can write your own build order, for example:
I've quickly written script to clarify the build order mentioned above and support most of modern Visual Studio versions.
Regards.