Yes.
Boosts stop after 999 HP and 99 for all stats. You can theoretically go over it with stat boosting items. The in practice max is 1038 HP and 101 for all stats if you get all available stat boosting items and use them at 998 HP and 98 in each stat . . . but that difference is not going to make or break anything.
Gotcha. Thanks!
The remake is fantastic, by the way, for anyone curious. Some QoL improvements, but it still retains the difficulty of the original for the most part (just like in the Gameboy version, I had to grind up some Agility around Venus's world, for example), and it's a blast. Went with Human (F), Mech, Mutant (M), and Monster this time around, and while I've struggled a bit with the monster, I've come to enjoy the balancing act of figuring out when to and when not to eat meat. I got lucky on the racetrack - I got the meat for all three bosses and my monster is no longer dead weight, it currently is the fastest party member I have, though not the strongest. My human has gotten ridiculously lucky with stat boosts - her HP is at 1005, her STR is in the high 80s, AGI is in the 60s, so for single target damage, she's by far my strongest. My mutant has been, conversely, pretty unlucky with stat ups - his MAG is only in the 40s along with his AGI around the same amount, though his HP is in the 900s at this point. My mech is getting less useful as the game goes on, but the built-in Mech status resists along with a high DEF rating has allowed it to tank some bosses while the more glass cannony people such as my mutant/esper whatever they're called in the remake Fires/Thunders/Blizzards them away.
I'm having a bit of a defense problem with everyone besides my Mech, however. I'm in Edo World right now, and there's some good armor there, but it is expensive as hell (and I spent a ton of money on upgrading my Mech, who was by that point in dire need of it). Still, though - the game is a blast, and reports of it being a lot slower than the GB originals are overstated, so long as you make sure to turn fast forward on. It's a zippy little game, otherwise.