Improving your effective Beast Heart Adept level
There are two classes in the game, Uncanny Trickster (Complete Scoundrel) and Legacy Champion (Weapons of Legacy) which, as a class feature, advance the class features and effective level of another class. Although it's sometimes considered cheesy and should definitely be run by your DM, there's nothing explicitly stopping these classes from advancing your effective Beast Heart Adept class level past 10.
Since the abilities granted to your Monstrous Companion occur on specific levels (rather than being derived from a mathematical formula that references your class level), increasing your effective Beast Heart Adept level past 10 won't typically make your companion any stronger. However, by my reading, you can use these classes to counteract the penalties to effective class level incurred by selecting an advanced companion.
For instance, a Ranger 5/Beast Heart Adept 10/Legacy Champion 5 (effective Beast Heart Adept level 14) could select a Wyvern as their companion, and it would still receive Improved Evasion, despite the -4 penalty incurred for Wyvern being an advanced companion choice.
This may not be an efficient use of levels from an optimization standpoint, but to the best of my knowledge, it is the only way to continue advancing your Monstrous Companion class feature with further class levels after finishing Beast Heart Adept.
Improving your companion in other ways
The best way to improve your companion via magic items is to equip it with magic items. Look into:
- Mouthpick weapons (Lords of Madness), which may be wielded via a creature's mouth, and combined with all non-bite natural attacks in a full attack routine.
- Necklace of Natural Attacks (Savage Species), to give your companion's natural attacks magical enhancement.
- Stat-boosting wondrous items, like a Belt of Giant Strength, which magically resize to fit their wearer (even if their wearer is not a shape that one normally associates with, say, belts).
Finally, something that isn't strictly allowed, but that I would allow as a house rule if I were DMing for this character: See if you can use the Share Soulmeld feat (Magic of Incarnum) to grant some of your Totemist goodies to your companion. Because it's not technically an animal companion, familiar, or mount, this doesn't work as-written, but it can't hurt to ask your DM.