It is absolutely possible, running parallel networks will be even added as a GUI option in the next RaspiBlitz release (FOSS bitcoin - lightning node package) which will also make C-lightning available.
See the issue about the parallel networks:
Here is a screenshot demonstrating running 5 LN nodes (3 C-lightning, 2 LND) on the three Bitcoin networks (mainnet, testnet and signet) on the same machine:
For LND need to carefully specify the ZMQ ports to not mix the block hashes of the networks via:
and for example:
in the bitcoin.conf.
The Bitcoin Core, Lightningd and LND binaries can be the same, but - if using systemd - different services are the best to be used for the specific network instances.
I found using one bitcoin.conf file is sufficient (as ports can be set with the network prefixes), but the LN implementations should have their dedicated config files per instance.
As it was mentioned C-lightning makes this easy by having different directories for each network by default.