No, You only get to flip 1.

The maximum amount of monster tokens that can be found in a tile is 4 at all times. This means that there is no scenario which you can "obtain" or "battle" more than 4 monster tokens from a single tile. This means that some quests or aggravating may cause monster tokens to shift during adventure phase.

When there are more than 4 monster tokens on a single tile, half of the monster tokens (rounded up) needs to be moved to an adjacent tile towards the city tile. The monster tokens that bleeds on to the adjacent tile is up to your party's discretion. Use this fact strategically.