Short answer, no, you can't. Pipes and structures on separate networks do not interact. One work-around I've done is to use shortcuts to import my pre-construction drainage layout into a new drawing, promote it, then change the network name to reflect the post-construction drainage layout and build my drainage changes into that model. I have pre-determined styles to separate existing pipes and structures from proposed pipes and structures. This moethod has worked well for me on several projects, some that include extensive existing drainage layouts.
different parts can refer to different alignments
By and large, pipes runs that connect to other pipe runs should be in the same network. For example, all the storm pipes draining to a common outlet should be in the same network. You can have each pipe run associated with it's own alignment, as Joe pointed out, but there are advantages to having them in the same network.
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