Bestial Challenge + Mounted Challenge

Another Huntmaster question:

Bestial Challenge (Ex)

Whenever a huntmaster issues a challenge, both he and his hunting pack gain the bonuses and penalties associated with his challenge.

This ability modifies the challenge ability.

Mounted Challenge (Ex): When ridden by a cavalier,

chargers gain half of the bonuses and penalties granted
by the cavalier’s challenge class feature. This ability
replaces share spells.

Would both abilities stack?

Another Huntmaster question:

Huntmaster wrote:

Bestial Challenge (Ex)

Whenever a huntmaster issues a challenge, both he and his hunting pack gain the bonuses and penalties associated with his challenge.

This ability modifies the challenge ability.

Charger wrote:

Mounted Challenge (Ex): When ridden by a cavalier,

chargers gain half of the bonuses and penalties granted
by the cavalier’s challenge class feature. This ability
replaces share spells.

Would both abilities stack?

Plain reading would say yes but because you can only select a dog or a bird, both of which are small creatures, and you have to be riding the animal for it to gain the benefits of Mounted Challenge, you might have some trouble getting them to be able to stack.

Edit:Sorry to necro this, I was searching for Mounted Challenge and this was the first result and I never looked at the date of posting, my bad.