Do you want to come over?
が一般的な言い方です。
放課後 =after school だったら
Do you want to come over after school?
（放課後うちに来ない？）
夕飯を食べに= for dinner だったら
Do you want to come over for dinner tonight?
（今日夜ご飯食べにうちに来ない？）
というようにも使えます！
参考になれば幸いです。
yumaさん
ご質問どうもありがとうございます。
下記の言い方ではいかがでしょうか。
Do you wanna hang out at my place (later)?
Do you wanna hang out at my place (after school)?
--- to hang out = （友達と）一緒に過ごす
--- at my place = うちで
非常にカジュアルで、砕けた言い方ですが、
若い人のうちは、友達同士ではよく使えそうな言い方です。
ご参考にしていただければ幸いです。
Why don't you ask your mom if you can come over to my house for awhile.
Let's go to my house and play.
Would you like to come over to my house?
Why don't you ask your mom if you can come over to my house for awhile.
Let's go to my house and play.
Wanna go to my house?
Can you come over to my house?
I want to invite you to come over to my house.
Let's go hang out at my house.
Would you like to come over to my house?
（私の家に来ませんか）
Why don't you ask your mom if you can come over to my house for awhile.
（お母さんに私の家に来てもいいか聞いてみたら）
Let's go to my house and play.
（私の家に行って遊ぼう）
Wanna go to my house?
（私の家に行きましょうか）
Can you come over to my house?
（私の家に来られますか）
I want to invite you to come over to my house.
（あなたを私の家にお招きしたいです）
Let's go hang out at my house.
（私の家で遊びましょう）
"Do you want to hang out after school?" This is one way to ask your friend if they want to come over to your house after school is finished and just hang out (chill).
"We can hang out at my place after school." This response is more of a suggestion that you can make to your friend. If they ask you what you want to do after school, you can respond with this answer.
"Do you want to hang out after school?"（放課後遊びませんか）
- これは放課後家に来て遊ばないかと友達を誘う言い方の一つです。
"We can hang out at my place after school."（放課後遊びませんか）
- これはどちらかと言うと提案です。放課後何をしたいかと尋ねられたときに、このように返すことができます。
To be with your friends and chill out together this is called 'hanging out' when talking about your house as well as saying 'my house' you can also say 'mine' or 'my place'
they would know you meant your house
Please come to my home after school so we can play video games.
How's about playing video games at my home after school?
Do you fancy playing video games at my home after school?
If you want to ask a school friend to come to your home and enjoy the afternoon together with you after school, you may ask him/her straightforwardly and politely to 'please' come to your home. You may add what you two will be doing together, such as playing video games. Doing so will leave no imagination in your friend's mind because the purpose of your invitation is clearly stated. To 'fancy' in this context means to 'want to do something'.
You may ask your school friend as follows:
Please come to my home after school so we can play video games.
or
How's about playing video games at my home after school?
or
Do you fancy playing video games at my home after school?
学校の友達を放課後家に来て遊ぼうと誘いたいなら、'Please come to my home'（家に来てください）と単刀直入に、丁寧にお願いできます。
例えばテレビゲームをするなど、何をするのかを加えることもできます。こうすることで、誘っている目的が明確に伝わります。
'fancy' はこの文脈では「～したい」の意味です。
次のように学校の友達を誘うことができます。
Please come to my home after school so we can play video games.
（放課後家に来てテレビゲームを一緒にしてください）
How's about playing video games at my home after school?
（放課後家で一緒にテレビゲームをしませんか）
Do you fancy playing video games at my home after school?
（放課後家で一緒にテレビゲームをしませんか）
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