Does the Besu client support Plasma?
I guess this question could also be asked about other clients such as Geth and Parity as well.
Plasma is not directly a client feature. It's an architecture to facilitate certain scenarios.
How a Plasma implementation is actually done is a separate issue and I don't think any Ethereum client has built-in Plasma support. It's just something that is built around the Ethereum infrastructure and therefore any client can be used.
Actually most of the functionality in Plasma is outside the blockchain and only some small interactions with the blockchain are required.
The Besu client supports
The Besu client supports common smart contract and Dapp development, deployment, and operational use cases, using tools such as Truffle, Remix, and web3j. The client supports common JSON-RPC API methods such as eth, net, web3, debug, and miner.
Besu doesn’t support key management inside the client. You can use EthSigner with Besu to provide access to your key store and sign transactions.