I am thinking about asking a detective brainteaser/riddle which would contain different parts. One part might tell you where to find the next clue. ie: You find a letter at the crime scene that tells has hidden clues telling you to go to a certain address. I was thinking that I could ask this question over a span of 10 or so days, a clue every 1 or 2 days. Would it be acceptable to put this question into several different parts (Murder - Part 1, Murder - Part 2, Murder - Part 3, etc.) or would that be looked upon badly by the community and receive downvotes?
As noted in comments, If each of the questions qualify as "questions" within this site's perspective, there should be no reason for it to be downvoted, referring to a previous question is rather a common trend followed in other questions asked by many.
By qualifying as "question" I and others mean each of them cannot be just clues and each of them are substantial enough to be questions. I think an example would help here
The above is a question where there are multiple riddles and they all come together to form a grand solution, but some of these riddles have already been solved in this site and some of them are so simple that if they are formed as questions, they may not be challenging enough, so I combined them.
As long as each question can be read and answered without referring to the other questions in the series, that's fine. There's nothing wrong with having a framing story that spans multiple questions.
If you need to have answered the previous questions to answer the next one, then no, that's not acceptable. Questions on Stack Exchange do not expire. Sooner or later, a vast majority of readers will be people who found the question in a web search, not people who read the question when you posted it. These people won't know or care about the series unless they happen to take an interest. It is part of the social contract when you post a question on Stack Exchange that your question should be useful for these future visitors.
If you have a series of questions, each of which builds on previous answers, a good way to satisfy both series-hoppers and individual-question-readers is to give all the relevant answers to previous episodes in a spoiler block. People who want to solve this question can read the spoiler block, and people who want to work the series can leave the spoiler hidden and jump to the first question.