I personally think that you CAN have too many tubes in the signal path, especially if they are capacitor coupled. As I've added more tubes to my systems, they've always become softer-sounding and more vague, and have lost detail.
I used to use the highly-rated Monarchy Audio M24 tube DAC in my system (direct-DAC outputs with Siemens E88CC gold-pin premium tubes), and that worked pretty well. But it was still a trade off in transient speed and bass articulation and extension. I preferred the Monarchy M24 on recordings with brass instruments, and the Apollo sans M24 for recordings using stringed instruments because it captured the transient speed of the strings better.
Then I obtained an exceptionally good 6SN7 prototype line stage and I have to say it is the best sounding tube preamp I've heard anytime in recent memory. So I sold the Monarchy M24 and run the Apollo's analog outputs straight into the new tube preamp. This provides the best overall results I've heard in my system. It sounds like a magnificent tube system, just from going through one dual-triode tube, and that's how I like it best.
I think it may lose a tiny amount of transient snap/impact directly compared to an all solid-state signal path, but what it does to capture the beautiful harmonic portraits of acoustic instruments more than makes up for that.