The ×1.5 damage multiplier does not stack with the ×1.5 damage multiplier from Magic Mushroom, from the combination of The Book of Belial and Blood of the Martyr, or itself (by using an item such as Diplopia, for example). However, it will stack with any other multipliers, such as Sacred Heart.
Synergies
Abyss: When Isaac uses Abyss to absorb Cricket's Head, it turns into a larger red locust dealing triple Isaac’s damage per tick.
Interactions
Haemolacria: Both 1.5× damage multipliers stack as expected.
In the original Binding of Isaac, this item was known as "Max's Head". Max was a non-existing animal named after the rabbit of Edmund McMillen's sister.
The filename for the item icon in the game files still refers to it as "Max's Head".
According to Edmund's first post-Repentance Lore Stream,[1] the reason for the name change is due to the fact that it 'bugged him' to name an item after an animal that did not exist in a game that was written around his life.
Cricket's Head is named after one of Ed's former cats who is now rehomed, Cricket.
According to Edmund's first post-Repentance Lore Stream, the reason for re-homing Cricket was that Cricket became increasingly moody after the death of one of Edmund's other cats named Guppy, which involved getting into fights with Tammy.
Although Cricket's Body and Cricket's Head are presumed to be from the same animal, Cricket's Body has darker fur color and spots than Cricket's Head.
Magic Mushroom, from the combination of 
The Book of Belial and 
Blood of the Martyr, or itself (by using an item such as 
Diplopia, for example). However, it will stack with any other multipliers, such as 
Sacred Heart.
Abyss: When Isaac uses Abyss to absorb Cricket's Head, it turns into a larger red locust dealing triple Isaac’s damage per tick.
Haemolacria: Both 1.5× damage multipliers stack as expected.
The Parasite - Pick up any 2 of the following items in a single run:
Bob's Rotten Head, 
Dead Cat, 
Cricket's Head, and 
Tammy's Head (
The filename for the item icon in the game files still refers to it as "Max's Head".
Cricket's Body and Cricket's Head are presumed to be from the same animal, Cricket's Body has darker fur color and spots than Cricket's Head.
Pet Items 
The Binding of Isaac: Rebirth
