Arguably, one of the most popular and beloved aspects of the Lamentations of the Flame Princess Rules & Magic book is the Summon spell. I mean, come on, you've got to love a first-level spell that lets you summon a randomized monster, often vastly overpowered, that can either eat you, serve you, or straight up end the world if you screw up badly enough.
However, sometimes you want to summon something a little more specific. Sometimes, you don't just want any demon, but specifically Headsosoth the Headsucking Monstrosity from Mars. Sometimes you want to summon a demon that can possess a pet bird and use its body to spy on the local mayor, as was the case in our game last Saturday.
Here's my house rule for handling that situation.
"Advanced Summon" is not technically a separate spell. When a Magic-User reaches a high enough experience level to cast ninth-level spells, the Magic-User can choose to memorize Summon as a ninth-level spell instead of a first-level spell. This version of the spell is considered Advanced Summon.
When casting Advanced Summon, the Magic-User must sacrifice at least one creature worth at least 2 HD total; this is not optional like it is for the regular Summon spell. The Magic-User must also make at least one thaumaturgic circle (again, not optional), and the thaumaturgic circles used for the Advanced Summon spell cost ten times as much as they do for the regular Summon spell (i.e. 5,000sp instead of 500sp). The sacrifices and thaumaturgic circles still aid in the domination roll, as usual.
Casting Advanced Summon takes one full hour (not including the set-up time of preparing the summon circle and killing the sacrifice).
Upon casting Advanced Summon, the Magic-User is allowed to choose the form of the demon from the table included in the Summon spell description; any available form can be chosen except for the results that would normally be possible if one were to roll a 20 on the table (Collective Unconscious Desire for Suicide, Disruption of the Universal Order, etc.). The Magic-User also gets to choose one appendage (adjective and noun) and one power from the corresponding tables in the Summon spell description, in addition to the appendages and powers that may be randomly rolled as usual. The Magic-User only gets to make these choices if they succeeded on their save vs. magic (Step 2 of the Summon casting process).
Other than the differences listed above, Advanced Summon works the same way as Summon.
Example: Mordamir the Twice Dead, a Level 20 Magic-User, spends 50,000sp to create 10 thaumaturgic circles, sacrifices 10 HD worth of prisoners from his seclusium's dungeon, and casts Advanced Summon over the course of an hour using a ninth-level spell slot. He attempts to summon a 20 HD monster. He succeeds on his save vs. magic. He chooses to summon an Orb of Light with Gossamer Feathers and the Memory Wipe ability. He also randomly rolled a Smoking Horn and the Victims Rise as Undead ability, so the creature has those features as well. Because of his level, his sacrifices, and his thaumaturgic circles, he gets a +35 bonus to his domination roll. He succeeds on the domination roll by double a Great Margin. Mordamir now controls an Orb of Light with gossamer feathers and a smoking horn bound permanently to his service, with the following stats: AC 12, MV 120', Morale 10, 20 HD, 1 attack (1d6 damage) that causes those it kills to rise again as undead, immunity to normal weapons, and the Memory Wipe ability.
If you're running a campaign in which the PCs are unlikely to ever make it to a high enough level to cast Advanced Summon, you can lower the spell level needed to cast the spell. You can also make Advanced Summon a completely separate spell that needs to be discovered or researched, if you so desire. I'm rather fond of the idea that one spell can have multiple methods of being cast, with multiple results.
In case you're wondering, the PCs in my campaign used Advanced Summon to obtain a demonic eyeball that mind-controlled a pigeon (after surgical replacement of one of the pigeon's eyes). The demon said it enjoyed its new avian body because it was amused by its lack of continence regarding waste expulsion. Demons are gross.