Can multiple cryptocurrencies achieve broad adoption at the same time?

Yes. We have multiples of very many things. If you have just a singular cryptocurrency, you will soon enough have a movement who would like to add features, etc. to it, and in turn start their own cryptocurrency, and this will happen a couple of times. So, yes, definitely, I think multiple crypto currencies will be widely adopted (perhaps nothing close to how widely adopted currency-notes are).

Even more so than the adoption we need to see how merchants and exchanges will adopt other multiple cryptocurrencies.