If you're looking for anime similar to Sore Ike! Anpanman Sukue! Kokorin to Kiseki no Hoshi, you might like these titles.
When a comet that comes back once in a hundred years, Dream Suisei, is travelling by Earth, everybody sees the same dream of a foreign world. Melonpanna saves an egg from being crushed and wakes up to find out that the egg has followed her home. A kitten hatches from the egg, and Melonpanna names her Nyanii and starts caring for her. But soon they find out that Nyanii is needed back on Dream Suisei, and if she doesn't return there, she will vanish. Melonpanna struggles with the upcoming hard goodbyes, but the real trouble starts when Baikinman accidentally awakens the evil monster Muuma.
The story begins in Anpanman World, where everybody is bustling around, getting ready for the annual Star Festival. On that day, an egg emerges from Baikinman's garbage box, and when it hatches, a mysterious boy named Kurun emerges from within. Though Kurun does not know where he came from, he spends his days having fun with everybody. But one day, black stars begin raining down. Anpanman thinks that something suspicious might be occurring at the Star of Life, and he heads there.