I asked him to ask his boss to sit with us in a meeting.
I asked him to have his boss sit with us in a meeting.
この場合は、次のように言うことができますよ。
ーI asked him to ask his boss to sit with us in a meeting.
「私は彼に彼の上司にも会議に同席するよう頼んだ」
to ask him to ask his boss to ... で「彼に彼の上司に…するよう頼む」と言えます。
to sit with us in a meeting で「会議に同席する」
ーI asked him to have his boss sit with us in a meeting.
「私は彼に彼の上司にも会議に同席するよう頼んだ」
to ask him to have his boss 動詞 で「彼にかの上司に…するよう頼む」とも言えます。
his bossの後ろをto不定詞にする必要はありません。
ご参考まで!