Is it possible to add non compaten pets like dogs or cats to the bridge interier?

sk8tor09

I know that in several episodes of TNG, Data has mentioned there being several cats including spot (his own cat) being on board the enterprise; and on more then one occasion we see caption Archers beagle Porthos in archers quarters and at least on one away mission; the Klingons have also been seen with a reptile like creature (possible torg) on board on a few occasions. Is it possible to add animals like dogs, cats, reptiles, or even birds that are native to the factions home world given that even as far back as the mid 22nd century star fleet has shone animals joining the crew for a short time? Maybe if it was possible to add one or two to the ship roster, a doff mission could be created were you assign a doff or random crewmember (come on there's at least 50 or so walking around each ship) that could take the dog to a park on the holodeck to let the dog get out some energy while your off battling the enemy. At the same time getting a random doff experience.