Context: full PoS with Casper CBC and sharding will require a verifiable randomness function that is secure and decentralized, in order to randomly select and assign validators, shuffle notaries, and select collation/block proposers. Such a VRF is an ongoing topic of research, and is yet to be specified and implemented.
Alternative approaches to scaling other than sharding include state channels, side chains, multi-chains and off-chain computation. Projects are included here in this summary spreadsheet by the Web3 Foundation. Parity Substrate is another project. Other designs and sources of inspiration include:
Potential sources of inspiration / other projects include:
Snowflake to Avalanche: A Novel Metastable Consensus Protocol Family for
Cryptocurrencies: it’s a probabilistic Byzantine fault tolerant (BFT) consensus protocol that is synchronous on paper, but has been developed on a real internet (which is partially synchronous at best).
Ziliqa: a PoW sharded architecture consisting of a dataflow smart contract layer, and 5 other layers. Uses the EC-Schnorr multiginature signature scheme. However, RANDAO is preferable to aggregate/multisignature schemes since it is not prone to a 51% attack. Also uses committees, as is planned with Dfinity and Ethereum, although here the committees manage how miners are assigned to shards, whereas in Ethereum that is the task of the beacon chain and the sharding manager contract on the main chain. Uses PBFT consensus, which doesn’t seem to be as good as Casper FFG, which is also used with PoW.
EOS: has a DPOS (delegated proof of stake) protocol. It experienced a liveness fault  and locked accounts to prevent theft just days after launch (which has spillover effects to other cryptocurrencies if exchanges decide to socialize losses from EOS, e.g. by freezing accounts of EOS and other cryptocurrencies and declaring bankruptcy, which in turn has legal implications ). It is controlled by a relatively centralised server and cartel of 21 block producers. It does not have a provably correct-by-construction, formally verified consensus protocol. It is very expensive with deposits instead of fees (deploying Cryptokitties on it at it’s peak would cost about $1.5b in staked deposits) [3, 4]. You need to pay to create an account, need EOS to buy RAM in order to make transactions. Need to stake EOS for CPU and network resources (IMO this is a necessary con, since without incentivizing resource use, a tragedy of the commons arises; see e.g https://eips.ethereum.org/EIPS/eip-908).