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Yes, you can:
Мы пошли гулять с Иваном, Петром и Игорем.
or
Мы с красивой девушкой гуляли по парку.

Actually, what I already wrote, the main part is "мы". (Or it can be "вы", "они" etc.)
What...

Oh, I see, you original sentence was "МY dog аnd i went for a walk with you". I did not notice "with you" part.

In this case, I would prefer "Мы с тобой пошли гулять с моей собакой". It sounds...

Sorry, I am afraid I do not fully understand this question. Can you be more specific?



You wrote "My dog and I" - so "Моя собака с тобой" is definitely incorrect.

Theoretically, you can say...

More elaboration: a word after "с" (a noun or a pronoun) should be in Instrumental.
The first word (e.g. "мы") does change with cases:

Мы с тобой работаем. - Nominative.
Эта книга будет полезна...

I think I understand what causes your confusion.
"Мы с тобой" can stand for "you (sg) and I" or for "you (sg) and us".
"Мы с вами" can stand for "you (pl) and I" or for "you (pl) and us".
"Мы с...