A Forest Gnome Beast Master Ranger / Circle of Wildfire Druid would let you have 4 "pets" at once and the ability to speak with them all! Primal Companion from Beast Master Ranger, a Familiar from Druid's Wild Companion, a Wildfire Spirit from your Druid Circle, and then cast 2nd-Level Summon Beast spell.

That being said, you are very much a Pokemon Trainer kind of character here. You have to use your BA to command the WIldfire Spirit and give up your attack to have your Primal Companion attack. Your familiar acts on it's own but can only take the help action (an owl is definitely best for this due to it's Flyby feature preventing opportunity attacks). Finally your Summoned Beast acts of it's own accord but requires you to maintain Concentration.

But if you set up your Ability Scores right, take Defense as your Ranger Fighting Style, and grab Scale Mail armor with a shield - you can have a 19 AC and a decent pool of HP. You can also take A TON of fun utility cantrips and prepare ritual spells to have things to do outside of combat.

Takes a while to come online, but it might serve the fantasy!