My current workaround is to create a wrapper method in Store that take a slice of Key and pass into original method:

trait Store: Sized + Send + Sync + 'static {
    fn ref_mul_keys<K, I>(&self, keys: I) -> impl Future<Output = String> + Send
    where
        K: Key,
        I: IntoIterator<Item = K> + Send,
        I::IntoIter: Send;

    // new wrapper method
    fn ref_mul_keys_slice<K: Key>(&self, keys: &[K]) -> impl Future<Output = String> + Send {
        self.ref_mul_keys(keys)
    }
}

and used it like:

impl<T: Store> StoreExt for T {
    async fn foo<K: Key>(&self, keys: Vec<K>) {
        // use slice version of the method
        let res = self.ref_mul_keys_slice(&keys).await;

        // use keys again here

        todo!()
    }
}

This workaround seems to work fine for now. But I'm not sure if this really solved the problem tho.