In construct state (usually) only the first noun is pluralized.
Birthday - יום הולדת, birthdays - ימי הולדת
Pet - חיית מחמד, pets - חיות מחמד
This is different from noun+adjective, in which both the noun and the adjective get a plural suffix:
A hot day - יום חם, hot days - ימים חמים
The word מחמד is rarely used outside the idiom חיות מחמד. A friendly animal is חיה חברותית or חיה נחמדה or חיה ידידותית. But there is also a grammar point here: the difference between a construct state and a noun + adjective combination. Note how the ה in חיה becomes ת in חית מחמד, this is because it's a construct. As radagastthebrown explained, when pluralising a construct, only the first word changes, whereas "friendly animals" are חיות נחמדות. And adding a definite article, in the construct, only the second word gets an article - חיות המחמד, but החיות הנחמדות.
@radagastthebrown 1. Strange that I can't response to a person who have responded to me, but anyway: 2. That fact that you have never heard this specific idiom/expression, doesn't necessarily means it doesn't exist, as I said = it's a hi-tech slang, and people who I have heard this expression from and friends of mine who work in other companies do know this expression. 3. Slang usually is not about respect someone. And even than - onone has to take it on their part. 4. Hebrew currently contains about 75-80K words, while most of peoples' vocabulary on a daily basis is about (English) ~5K, so I am guessing there are a lot's of words you and me have never heard before. :) BR,