Did some more brainstorming last night.
A typical campaign would play like a combat-centered Call of Cthulhu adventure, with the investigators starting on a rather normal crime case and then uncovering clues that sees them unravelling a fiendish plot that culminates in a big showdown with the mastermind / big otherworldy beast.
So after finding the first clues in the 1st mission, they can then proceed to a choice of 2nd missions, depending on which clues they found. There, they find more clues, and when they have all the required pieces, they can attempt to solve the case by "unlocking" the last scenario. A campaign would have from 4-6 scenarios, with each one having a playtime of 45 mins - 1 hour each.
The board gets deivided into 4x4 or 3x3 regions, with buildings being their own seperate regions.
The "starting row", a.k.a. the table edge where the investigators start has no clues tokens.
Before starting, a number of clue tokens as specified by the scenario along with a number of blank ones are put into a draw bag, mixed, then a few are discarded again, this means that players can never be sure how many clues are in there. Example: put 5 tokens of Case A and 9 blank tokens into the bag, then remove 3. The bag now contains 12 tokens total (one for each of the 12 board regions sans starting row), with 3-5 clues and the rest being blanks, or maybe random occurences.
Clues tokens are uncoverd when they are in line of sight, with certain effects limiting the sight range (rain, fog, nighttime). This would of course also have an effect in combat.
If the token is an enemy or group of enemies (or even NPCs), they are placed immediately and combat starts. The players may roll some sort of reaction check to see if they can ambush the encountered group (or vice versa).
Otherwise, the clue must be investigated by moving into contact with it (for example, it might be a bloated body, with the cause of death being drowning... Even though there's no body of water for miles around! This would be one clue).
When all clue tokens have been resolved, the scenario ends and the investigators can use the collected tokens at their headquarters (police station or whatever) to see if they can find out more, interrogate suspects, or ask for an increase in their budget.
Each player would control one character, and may add an agent or civilian in the course of the campaign, depending on who they meet and persuade to help. Some characters may even have an ally at the start of the game (think of "Ashcan" Pete and his dog in Arkham Horror).