OB1
Jedi Master
The UA also, and this was another big thing I liked, allowed the companion to noticeably grow in strength. Not just "here's 4 hp every level" but actually increasing it's stats and allowing a companion that has been with a legendary figure t itself be far physically and even mentally superior to others of its kind.
But this is already the case, only the PHB Ranger is able to do it with a new animal with just 8 hours of mystical bonding
Regular Hawk - HP 1, AC 13, Talons +5, 1 dmg, Perception +4
20 Level Ranger Hawk Companion - HP 80, AC 19, Talons +11, 7 dmg, Perception +10
Regular Giant Wolf Spider - HP 11, AC 13, Bite +3, 1d6 dmg, Perception +3, Stealth +7
20th Level Ranger Gian Wolf Spider - HP 80, AC 19, Bite +9, 1d6+6 dmg, Perception +9, Stealth +13
Those both seem like pretty legendary versions of the beasts to me. That said, when I was thinking about it, I realized there is a way to provide more options for the way to play the Beastmaster without needing a revision or errata to the class. Just add some new spells. It seems that since Xanathar's Guide did the expanded Ranger spell list, people's concern about the Hunter Ranger went down.
What if a set of Beast Master specific spells were published? The added bonus here being that even if you are currently playing a Beastmaster you could add these spells when you level up. Here is a first draft of what I think these could look like. Because spells known are such a precious resource to a Ranger, I've tried to make these really worth the cost for a player wanting to beef up their animal companion.
1st Level Ranger Spells
Command Beast - 1 Min, Concentration, Bonus Action, self - When you cast this spell, you gain an additional action that you can use only to command your Beast Companion
Protect Beast - Action, Touch - You touch a beast and it gains 2 times your level in temporary Hit Points
2nd Level Ranger Spells
Revivify Beast - Action, Touch - You touch a beast that has beed dead for less than 1 minute and it returns to life with 1 HP
Alter Beast - Action, Touch, 1 Hour - You touch a beast and it gains one of the following benefits, It's natural weapons become + 1 magical weapons, It's AC increases by 2, the DC of any of it's abilities increases by the caster's proficiency bonus
3rd Level Ranger Spells
Find Greater Companion - 1 Hour Casting time - You call out to the wild to find a new beast companion that can be Large and of a CR equal to 1/4 of your level (rounded down). The beast must be native to the area that you are in and able to reach your location. If you are in your favored terrain, you pick the beast that appears, otherwise the DM chooses from what is appropriate for the area.
4th Level Ranger Spells
Awakened Beast - 1 Hour Casting Time, Permanent Duration - You forge a permanent telepathic bond with your companion. As long as you are on the same plane of existence, you can communicate telepathically as well as see through each others eyes at will. The beast can also add 6 points to it's ability scores, either all to one or split between several. The awakening lasts until your companion is killed. If later brought back to life, the spell must be cast again.
Reincarnate Beast - 1 Hour Casting Time, Permanent - You focus on the spirit of a beast dead for not more than 30 days. The beast is reincarnated, appearing from nearby at the end of the 1 hour casting time.
5th Level Ranger Spells
Heroic Beast - Action, Touch, 1 Hour - You touch a beast and it gains all of the following benefits. 4 Times your level in Temporary Hit points, natural weapons become +3 magical weapons, AC increases by 5, DC of any of it's abilities increase by casters proficiency bonus and it is Hasted per the spell. You also gain an additional action that you can use only to command your beast companion.
Unless... you refuse to call it a problem.
The real question is: can lots of groups handle one player with two characters?
I bet the answer is an unreserved "yes".
Sure, the group I play in (rather than DM) has a "bicycle" character that we roll to see who is playing at the beginning of each session. Our very own "pet" Goliath Barbarian. Of course, he get's added into the encounter math and get's his share of the treasure and xp. Would your PC power level animal companion do the same?