Artifact unaligned pair of lenses The Lens of Truth, from Zelda, which grants see invisible when worn.

In variants with percentage-based intrinsics, see invisible is no longer a binary attribute. Eating invisible stalkers now gives you various percentages of the intrinsic. While extrinsic see invisible still works like it does now, allowing you to see any invisible monster in line of sight, intrinsic see invisible shows you invisible monsters in line of sight within a certain radius from you. The radius increases with the percentage, possibly the square root of the percentage (so 64% see invisible is a radius of 8, and 100% is a radius of 10 - note that 100% still is less powerful than extrinsic see invisible’s unlimited range).

Make see invisible an instantaneous effect rather than an intrinsic. After seeing invisible for one turn, players must guess where invisible monsters are (or use something to get more see invisible effects).

The Eyes of the Overworld (or perhaps anything that grants astral vision) allows you to see anything invisible within the astral vision radius.

Nazgul can innately see invisible.

Cure blindness is a pretty useless spell, and should probably be removed or its effects folded into some other spell like extra healing or clairvoyance. Alternatively, if see invisible is nerfed so that it cannot be granted permanently, this could be folded into a “spell of true sight”, which grants temporary see invisible as well as curing blindness, perhaps temporary blindness resistance, and blocking (but not curing) hallucinations like Grayswandir’s wield effect.

Monster spell that either generally or specifically debuffs the player. It targets beneficial timing-out intrinsics you have, such as speed, detect monsters, and see invisible, and reduces their time remaining, possibly removing them outright. Does not affect permanent intrinsics or extrinsics.

A spell that provides see invisible (but the potion should be objectively better than it by at least an order of magnitude).

Stalker corpses don’t confer see invisible anymore, and have their odds of conferring invisibility decreased from 100%.

Quaffing cursed invisibility removes the invisibility intrinsic if you had it. Possibly the same for see invisible.

Rings carried by Nazgul are all artifact rings of invisibility. They autocurse and also confer telepathy, see invisible and aggravate monster.

Intrinsic see invisible now works only at a range of 2-3 squares. Extrinsic see invisible works at the current see invisible range (unlimited as long as you can see the space normally).

The cursed potion of see invisible removes any see invisible intrinsic that the player has.

A new “illusion” or “disguise self” monster spell, which makes the caster or an allied monster appear as another monster of its choice until something disrupts the illusion (it gets attacked, otherwise takes damage, or it makes an attack). Monsters specifically cast it when you cannot see the target monster. It might be possible to implement this spell to be player-castable as well, but this would be less effective. (you could use it to fool monsters into thinking you’re another hostile monster so they don’t attack you, but not much else).

The illusion favors nasty monsters, but low-level spellcasters may only be able to create illusions of somewhat higher-difficulty monsters. A potentially evil addendum is that high-level spellcasters may use the spell to make themselves or other powerful monsters appear to be weaker monsters.

Perhaps if you have extrinsic see invisible (and only extrinsic), you can see through such illusions.

See invisible operates on a scale that determines what level of invisible monsters the player is allowed to see. (A low-level monster that drinks a potion of invisibility should be visible even with weak see invisible, an arch-lich casting disappear should require very strong see invisible.) Invisibility should do this too and have a scale as well (one notable place on the scale being that invisibility is kept only until the invisible thing takes an offensive action). If rings of invisibility and see invisible are made chargeable, this is an obvious avenue for them.

The timeouts for intrinsic invisibility and see invisible from eating a stalker corpse should be very long.