V/A+ 는다면/ㄴ다면/다면 V+ 을/ㄹ 수 있을까요?

It is used when the speaker asks very carefully, considering the situation facing the listener. You should use ‘-는다면/ㄴ다면/다면’ of assumption together in the preceding clause to consider the listener’s situation.

For ‘-는다면/ㄴ다면/다면’. if the stem of an action verb ends with a consonant, you use ‘-는다면’, with a vowel, you use ‘-ㄴ다면’. After the stem of a descriptive verb, you use ‘-다면’.

For ‘-을/ㄹ 수 있을까요?’, if the stem of an action verb ends with a vowel or ‘ㄹ’, you should use ‘-ㄹ 수 있을까요?’, with another consonant, you use ‘-을 수 있을까요?’.

실례가 안 된다면 개인적인 질문을 하나 할 수 있을까요?
If you don’t mind, can I ask you a personal question?

혹시 문제가 안 된다면 이 표를 다른 공연 표로 바꿀 수 있을까요?
If it doesn’t matter, can I change this ticket to another performance ticket?

지금 바쁘시지 않다면 한 5분 정도만 더 기다려 주실 수 있을까요?
If you’re not busy right now, could you wait another five minutes?

Conversation:

체크인하려고요. 여기 신분증요.
I’d like to check-in. Here’s my ID.

네, 예약 확인되셨습니다. 더블 룸으로 2박 예약하신 것 맞으십니까?
Okay, your reservation has been confirmed. You have a reservation for two nights in a double room, right?

저는 트윈 룸으로 예약했는데요. 메일로 받은 예약 확인서를 보여 드릴게요.
I had a reservation for a twin room. Let me show you the confirmation of the reservation I received by e-mail.

그렇네요. 저희 쪽에서 무슨 착오가 있었나 봅니다.
You’re right. There must have been some mistake on our side.

예약하신 대로 트윈 룸으로 방을 배정해 드리겠습니다.
I will assign you a twin room as you have reserved.

네, 그런데 혹시 괜찮다면 고층으로 방을 배정받을 수 있을까요?
Okay. but if it’s okay, can I have a room assigned to a high-rise?

그럼요. 저희가 절차상 고객님의 신분증을 복사해야 하는데 괜찮으신가요?
Sure. We need to copy your ID card for the procedure. Are you fine with that?

그리고 고객님 본인 명의의 신용카드도 필요합니다.
And we also need your credit card in your name.

Related words
체크인 check-in
예약 확인서 confirmation of the reservation (It refers to a written article or document to confirm the fact that a reservation is made.)
배정 to assign
절차상 for a procedure (It indicates the aspect of order or method to make work done.)
명의 name

Source: Yonsei University. Korean Language Institute