There is not a naive way to have a conditional multi select drop down in Field B. By that I mean that if the user chooses Dog, then a conditional drop down can offer up only Dogs breeds, and then the use may select 1 dog. and that can be the field Choice 1.
Then you can have a separate Conditional drop down, also set by the same initial selection of Dogs in field A, and then the user can once again choose a Dog breed as Choice 2.
same for choice 3.
Then if you like you can use a formula field to concatenate them all together n a comma separated list.