First off, additional bonuses... bonuses being things like CTR, ASI, +damage, +damage to ______, MSI. Some of the ones I'm going to list have been thought of before, like health-governed things or shield properties, but if I'm going to make a list of possible new properties, I decided I might as well include them.

Status Strength: Alter the overall power of a status. (Strong Poison lasts longer and is more debilitating than Weak Poison.)

Status Duration: Increase/decrease the length of statuses, but weaken/strengthen the status's effect. Basically, it goes like this: you take Poison, but you have a duration bonus on that makes it last for a shorter amount of time, but the poison weakens your attack and defense more than normal. Or if you take Fire and have a +Duration instead of a -Duration, the fire lasts longer but deals slightly less damage per tick than it would normally.

Freeze would be excluded from duration effects, given the only adverse effect it causes other than immobility is damage when the afflicted enemy thaws by the timer hitting 0 as opposed to taking damage or another enemy's attack thawing it out. Additionally, I don't think players themselves take thaw damage, so... yeah.

Projectile Speed: Increase or decrease the speed of projectiles. Only found on weapons that shoot projectiles, of course; you wouldn't find this on a Rocket Hammer or Troika.

Projectiles Range: Increase the range of projectiles shot. Not found on items with no projectiles.

+/- Defense VS. _______: Modify the damage you take when the attacker is of a certain monster family.

+/- ______ When Health Is ______: Change any variety of things (+/- defense, +/- damage, +/- movement speed, etc.) when the player's health is within a certain range. For example, +MSI when health is 1/4 or lower, or +Damage when at full health.

Shield Repair Speed: Modify the speed at which your shield is usable again after being completely broken.

Shield Regeneration Speed: Modify how quickly your shield can get back to full health.

Bomb Radius: Change the range of bomb effects.

Bomb Fuse Time: Increase or decrease the time it takes for a bomb to detonate after being planted.

Damage to ______ when using a ______: Modify damage dealt when attacking a certain monster family with a certain weapon type.

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Now for something else entirely; choosing what your heat does to your gear besides increase its overall strength. I believe this has been suggested before, but I'd rather not necro a topic...

Basically, at heat 5 and 10, have a variety of options to choose from instead of it always being +Health to armor and CTR for weapons. In other words, I could have a Triglav with ASI Medium instead of CTR Medium, or a Magma Driver with CTR Low and Damage Low.

I'd also like to see things like +Damage to ______, but with each 'point' being worth a Medium instead of a Low. Concerning shields, they don't get any bonuses besides improving how much they can take before breaking; what if they could get a +Low to a defense type/status resist of the player's choice or to its overall health... or boost how quickly it repairs itself when broken or recovers from damage (see above)?

EDIT: Added some more possible effects.