No; however, you do have to pay to adopt more than one.
Go to your Fotos and look for the pet then click the pet's name and then re-buy the pet.
You may not adopt a free pet if you already have a pet in your possession. If you desire to have more than one FooPets pet, you must purchase one from the Foo Shelter, the Premium section, or from a breeder in the Breeding Forum.
Go to your play page and then click "Adopt foopets"
In order to get a FooPets pet that is one year old, or older, you must either adopt the pet from the Shelter section of FooPets or adopt from another member in the forums. Alternatively, you may accelerate the age of one of your own pets. They will automatically be aged to 1 year, for a fee of 20 FooDollars (the virtual currency used at FooPets).
Check the breeding forum or go to adopt foopets on the play page
If by this you mean virtual a pet, you can join a website called FooPets where you can adopt puppies or kittens. You can also download an application from this website called the 'FooPets Desktop'.
It's easy! Just go to FooPets.com, and pick a pet. Then select "Adopt Now" and finish the process.
Dream foopets is a website where you can adopt REAL pets for free.
You can easily sell your pet to the adoption center, it will give you back a certain amount of foo Dollars based on your pet's stats. Others can adopt it if they wish.
Simple... Adopt it!
You can.