A rescheduling message needs enough detail to identify the original plan. "Can we change our meeting?" may be unclear if several meetings are approaching. Try, "Could we move our study meeting scheduled for Wednesday at two?"
Add a brief reason if helpful: "I now have a work commitment at that time." Then offer real alternatives: "I am available Thursday between ten and twelve, or Friday after three. Would either period suit you?"
Keep the status of the plan clear
Proposed alternatives are not automatically a new booking. After receiving an answer, confirm the chosen slot: "Thanks. Thursday at eleven works for me. I will update the invitation." State a time zone if participants need one.
If the change is close to the meeting time, use an appropriate channel the other person is likely to see. Follow any relevant cancellation or booking rules. A message alone does not necessarily change a paid reservation or an organizational calendar.
Practice rewriting the request without an unnecessary long explanation. Preserve the original date, the need to change it, and the available alternatives. Ask a partner to identify the current arrangement after reading the exchange. If they cannot tell whether Wednesday still stands, add an explicit confirmation or cancellation rather than assuming the other person will infer the change.