Not all factions within a city can be raised without impacting another. But Qeynos primary factions and Neriak primary factions are pretty much independent; the two cities are far enough apart not to be considered hostile, although obviously a priestess of Innoruuk isn't going to get into the Temple of Nife.
Some Neriak factions - Dark Bargainers - can be raised easily with Lightstones by the gypsies in... well, somewhere in the Desert of Ro these days. Then when you can get in, there's a wine quest that is basically "buying" faction like the famous Muffins quest. Before I knew that though... well... I got a lot of laughter from passing Tier'dal PCs who saw me slaughtering endless numbers of rats in Neriak. (GAH what a slow rate that was - about 1/10 had whiskers, 4 whiskers per turn-in, per one faction point or so).
Other Neriak factions cannot be raised without an equivalent drop in the same city. E.g. Cristanos Thex, the Queen's faction, is in direct opposition to Naythox Thex (the King). Neriak is about the only city I know of where you can be amiable in one part of the zone and KOS in another.
Qeynos Guard faction is very easy, just depopulate Blackburrow.
My greatest challenge was getting Licinia on max ally (which still isn't Ally without an Illusion or Collaboration spell) with all Cabilis faction except the necromancers. Crusader Quarg killed her several times even in Illusion:Iksar form (which used to be a painful quest in the TLC days).
So, as part of her RP, Licinia is an official ambassador from Qeynos to Cabilis, and a go-between / envoy to Neriak (from both Antonius and Kane - although Licinia doesn't know Kane is evil - I worked some quests to get Kane's faction up then repaired faction on the Antonius / Guard side... funnily she is Ally to the Guard, and Amiable to the Corrupt Guard, which is pretty funny for some Investigator subquests as a mob that pops and is supposed to attack you just smiles at you Amiably

)
My hat would be off to any Drakkin who tried to get Ring of Scale faction to maximum ally. It can be done without being evil, by killing Mistmore's old creations in his castle. I'd be curious to see if someone who went on a festival of bard-killing to get to Mayong Mistmore Ally, would in fact not be KOS when confronting him in the Theatre of Blood? I doubt it though - SOE ignores the old factions when designing the new ones.