Can you command it otherwise? Yup.
We can see from your quote that if you command the beast (with some cajoling, perhaps; it does consume your action) to Attack/Dash/Disengage/Help, the animal will do so.
If you do not command the beast anything, it will Dodge.
What, then, if you command it other than Attack/Dash/Disengage/Help?
RAW: nothing special.
There's no special rule saying what happens if you command the animal to Hide, so the usual rules are in play: the GM decides what happens.
What should the GM decide?
We can see, structurally, that the developers thought that commanding the animal to do "useful" things should take your action, so as to avoid wrecking the action economy. See many articles and guides and posts abounding on the internet regarding "summoners" in 3.Xe and 4e for many of the reasons why this was on their mind.
We also know, from many 5e player surveys and Unearthed Arcana attempts to revise Rangers, that the PHB ranger is... underwhelming.
All that's to say: it'd be reasonable to say that you have to use your action to command the animal to take any of the standard (listed) combat actions. It'd be reasonable to say that you can freely command the other actions, as they're not that impactful anyway. (Hiding one round to attack with advantage another round isn't a huge difference, numerically, from just attacking twice. It may be different tactically, though....) It'd be reasonable to say "I don't like how companions/summonees screw with spotlight time, so I'm going to ask you to kindly restrict yourself to the listed actions."