Parallel mining/ split hashrate? possible! merged mining? is also possible but only limited coins that support merged mining such as Namecoin, sys, and a few others that phill mentioned above, there could be more, but the key here, the coin needs to support merged mining, in a nutshell, small coins have merged mining enabled to make their blockchain more secured, their blockchain is referenced in BTC's blockchain, to be specific it's saved as a transition in the BTC block itself.

This gives them a somehow secured blockchain at almost no cost, the downside, all these coins are worth little to nothing, so the rewards are almost nothing, I just checked my mining account on Viabtc (which I longer use), and it has 2.5BTC cumulative mining rewards, some NMC, SYS, EMC and ELA, the current value of all these merged mined coins is below $20, maybe at some point in the past bull cycle they were worth $100, but this was obtained after years of mining on the same pool, would I take $10 for every 1BTC mined? why not, would I bother switching pools just to get them? probably not.