The good news is that LinkedIn is the place to put as much informationas possible about your professional self. Recruiters and HR representatives search specifically for any job they are hiring for, so the more detail you have, the more likely you will come up in their search results. The initial summary should include the most important information about yourself and your qualities; this should span relevance for both positions. Include information specific to you. Be sure to specify what qualities you offer and how you can add value to others. Unless you are searching for jobs at complete opposite sides of the spectrum, like Arts and engineering, it should only be an extra plus that you have qualities outside of the immediate job requested.
The most editing will be done to the past career experience. This is where most of the important information will be located. Do not shy away from putting all jobs you have had in the past here, you never know when it may be helpful. There is even a possibility that the extra, seemingly non-relevant job experience you have is exactly what they are looking for. Perhaps the customer service experience gained in the job as a server in college will come in handy for your marketing position. However, the details from that job may not need to be as elaborate as the job experience that can get you to your next position. If you are looking at two different career paths, include information that is relevant to both. Tasks within each job should be tweaked and geared towards the position you are looking for, with plenty of keywords. This can be done for two different positions; it is all about wording. Find ways to use the same task, worded differently for different positions.
A LinkedIn profile takes time and effort to edit, just like a resume or CV, and that is especially so if you are looking at more than one career path. It is not impossible though. LinkedIn allows for some leeway, as there is no page limit for the information you want to include. It should be noted though, if you are looking at different career paths, choosing two that are completely unrelated to each other or unrelated to any experience you have, may be extremely difficult. If you are unsure of the marketing department you want to be in, that is much different than wondering if you should become a doctor or an astronaut. Be realistic in your expectations but not discouraged!