Will it degrade performance? Possibly.
Each splitter, if they are 2-way splitters and properly balanced, will remove -3.5 dB of signal.
Downstream power: DOCSIS limits indicate -15..+15 dbmV
Carrier to noise: Depends on your provider but is usually between 30..40 dB range
Upstream power: also Depends on your provider but anything over 30 dBmV range should be good.
If your downstream or Carrier to Noise ratio ends up out of spec it could affect your stability.
I've seen modems work fine off of 3-4 splits... (each split removing -3.5 dB comes to -14 dB removal.. which means the signal was probably 'hot' to begin with) and some modems work horribly off of 1 split (probably a weak signal to begin with).
3-way, 4-way, 8-way splitters of course will remove different levels of signal. Best bet? Try and see 🙂 If you can't get off the first split, and you do end up with bad signal, call your provider. They should be able to run you a connection off the ground block, but it will cost ya.