`NetNestOperator` with custom input / output ports

I’d like to use NetNestOperator on a NetGraph that has custom input / output port names, such as

net = NetGraph[<|"y" -> LinearLayer[1]|>, {NetPort["x"] -> "y" -> NetPort["x"]}, "x" -> {1}] 

This should be doable, since there’s a one-to-one mapping between the input and output port names (in this case, they are identical), but Mathematica complains when I try for example NetNestOperator[net,2]:

NetGraph::netinvgport: Input is neither a valid input or output port for the given NetGraph.

Of course, for this simple example using

net = NetGraph[<|"y" -> LinearLayer[1]|>, {NetPort["Input"] -> "y" -> NetPort["Output"]}, "Input" -> {1}] 

works just fine, but

  1. There’s no way to generalize this to multiple inputs and outputs (i.e. using "Input1", "Input2", … and "Output1", "Output2", … doesn’t work)
  2. Custom port names are nice!

Is there maybe an undocumented option specifying the port mappings in NetNestOperator?