Attach an EnsPlugin to an existing Prvider's network

[PierreJeanjacquot]

Is there a way to attach a plugin to the network object attached to an already instantiated Provider?

import { Network, EnsPlugin, JsonRpcProvider } from "ethers";

// already existing Provider connected to chain 134 (simulates provider injected by third party code, here a JsonRpcProvider but can be any kind of Provider)
const provider = new JsonRpcProvider("https://bellecour.iex.ec");
await provider.getNetwork(); // this make sure the network has already been detected

// --- our code ---

// registers network 134 as "bellecour" with a custom ENS registry
const bellecourNetwork = new Network("bellecour", 134).attachPlugin(
  new EnsPlugin("0x5f5B93fca68c9C79318d1F3868A354EE67D8c006", 134)
);
Network.register(bellecourNetwork.chainId, () => bellecourNetwork);
Network.register(bellecourNetwork.name, () => bellecourNetwork);

// network is correctly detected
await provider
  ._detectNetwork()
  .then((network) => console.log("_detectNetwork", network.toJSON()));
// _detectNetwork { name: 'bellecour', chainId: '134' } OK

// but the provider's network is not updated
await provider
  .getNetwork()
  .then((network) => console.log("getNetwork", network.toJSON()));
// getNetwork { name: 'unknown', chainId: '134' }

In this snippet, I would like to have the provider updated with the newly registered Network.
My main goal is to add ENS capabilities to the provider without having to create a new one.

Any idea?