Why would you do this?
Most reasons should be easily solvable by using an RPC call instead of a second deamon, isn't it?
I am trying to understand, for example, whether somebody could run 10 bitcoin full nodes only using one single copy of the blockchain thus saving on storage costs.
More specifically, I want to understand whether it is possible to prevent this behavior if it is already possible.
Now you are asking the correct question. The answer is, yes its possible to fake e.g. 10 full nodes while only providing the resources (or only slightly more) of a single node. The 9 fake nodes would run custom software (not core!) that would forward the requests to the single full node. In theory this full node can be any other on the network that is available, so you could do this without running a single node.
The idea to proof that you run a full node and thus get rewarded for doing so has been brought up several times. I have not seen a good solution yet. I would applaud a solution as the number of nodes decreases and the costs of running one increase.