Not sure if this is what you're asking, but you can easily install multiple blockchain nodes on the same computer software-wise, so long as they don't use the network ports: the procedure for installing 10 different nodes is no different for each installation than if you were installing one. The only wrinkle might be if you're doing something like using two forks of the same protocol using the same node software (such as Ethereum and Ethereum Classic).
You do not need to store the entire ledger/blockchain on every computer. You can store an abridged version of it that only includes the final state (plus some recent history in case of temporary forks). In fact, if your Ethereum wallet is "only" occupying 11GB, it sounds like that's already what you're doing. The full Ethereum blockchain is nearly 200 GB (here is the growth rate).
Most/all cryptocurrencies are designed to have transactions, and therefore their respective blockchains, be efficiently verified by lower-end hardware such as a cell phone. In fact, to allow such devices to sync to the blockchain, they need to be able to process more blocks per second than the number of blocks the currencies' protocol produces per second. For example, with Bitcoin, with its 10 minute block time (0.002 blocks per second), phones can handle several thousand times more blocks per second than are produced.
GPUs don't need to factor into an estimate of whether nodes can process all the traffic. Now, consider desktop computers are an order or two of magnitude faster (10x to 100x) faster than a cell phone. A desktop computer easily has enough processing power to handle multiple blockchains at the same time. Storage might get expensive for the average person, but one can use light clients, centralized services, or pruned data (see answer number 2 above).
If you mean to ask if there's enough computing power for mining in terms of letting the chain progress, the answer is yes: most, if not all, mineable cryptocurrencies have adjustment factors to account for more/few miners. However, there is a caveat: the more GPU-efficient protocols that mining is spread evenly over, the easier it becomes to attack some cryptocurrencies: if there are 1000 competing (GPU-efficient-to-mine) chains, by the pigeonhole principle, there exists at least one individual chain that can be attacked with 1/1000th of GPU power required to attack every chain at once -- i.e., an attacker who has 1/1999th of the GPU power used for mining can now launch a 51% attack on at least one currency. There are economic and social ways to mitigate this, but that's a much longer question.