I've got a medium Snoozer Lookout which as you can see is really big. This is Gracie and Sugar and Caren's (sims8813) Mia in it yesterday and we had 4 in it some of the time with enough room.
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I also have an Animal Matters console seat. Here is Sugar in it.
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As far as bags if you're just looking for one to use at the park you might like a messenger style. I got mine at Tinkerbell's Closet and I love it.
In this picture I'm carrying Sugar but you can see the bag. I'm the tall one in a white tee shirt.
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Here is a close up-
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Don't let his silly expression fool you- he loves it. We had a YT meetup yesterday and I couldn't get him out of his bag the whole day.
Welcome to YT!
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"If you have men who will exclude any of God’s creatures from the shelter of compassion and pity, you will have men who will deal likewise with their fellow men." — St. Francis of Assisi, 1181-1226