For the OP, I use a different bass for E flat.
Beyond your question, I have a few 4-strings with detuners, a 4-string tuned to DGCF and a 5-string, all relatively inexpensive instruments. In the past, there was a time when I was using only a 5-string, then only a 4-string tuned DGCF, which was fun to figure out and accomplish. In terms of things I was playing most, I found that E and E flat were most common tunings/keys with some D, and only a few things (that I’ve been doing) require anything lower. In the past few years, I added extra instruments with various tunings, and found I was happier working on things in the same tuning as they were done, particularly where open strings are involved—it’s possible to accomplish nearly anything otherwise, but I enjoy it most when my bass is set up the same. Even with the detuners and 5-string, I still tend to mostly choose the bass in the same tuning as the version of the song I’m working on, but sometimes I’ll try it on a different tuning as a challenge. The separate E flat bass will allow you to set the string gauges and action on each of your basses better for the tuning, and it’s easy to just grab the other bass when you need it. My 4-strings are all similar to each other in setup/quality so the difference is mostly about the tuning, I like them all, and there is not much difference in preferring to play one over another, so “similarity” can be a consideration in choosing an extra bass.