Taken from Korean Grammar In Use – Beginning – English Version, page 211, track 134:
A: 퇴근 후에 술 한잔할까요?
A: Would you like to go for a drink after work?
B: 미안해요. 오늘 약속이 있어요. 다음에 같이해요.
B: Sorry. Today I have other plans. Let’s do it next time.
I looked up 같이하다 on Naver English-Korean Dictionary (http://endic.naver.com/) because I didn’t know 같이 (together) and 하다 (to do) can be written together to form a verb.😀
At the top of the page, you can see 연관검색어 or “related search terms” which is useful to give you the synonyms or to grasp “the image” of the word you’re looking for.
In my case, I’m assuming that the word 동행하다 (同行, to go together) and 동참하다 (同参, to join or to participate) fit the definition of 같이하다 that is mentioned in the KGIU textbook. So 다음에 같이해요 actually means “I’ll join you guys next time”. ###