I'm not sure of the requirements for engineering but it could be possible. Medicine for example is possible from any degree as long as the pre-requisite subjects are met. So say you end up in Bachelor of Commerce and want to get into medicine, you would do the subjects for you majors in B.Com then do the pre-requisite subjects for medicine as your breadth and/or extra subjects. You would end up graduating with a B.Com degree in your chosen major and can then choose if you want to pursue medicine or a commerce post-graduate course.
As for engineering, I'm not the most knowledgeable when it comes to this area. However I have friends doing various engineering courses. I know that Chemical Engineers generally get paid the most and is really broad. There are many jobs you can get with Chemical Engineering such as working for pharmaceutical companies, oil companies etc. Again I will leave this area to more knowledgeable ANer's.
I'll do my best to help explain how courses work. Each course has many different subjects that relate to that course. Since you are restricted by credit points, which each core subject and breadth subject gives, it would make sense to choose the course that you are interested in to maximise the amount of subjects you can do in that chosen course. Say you like Science subjects. If you were to choose B.Com instead of B.Sci, you would be limited to only 6 science subjects whereas in Science, you could have roughly 18 science subjects. At UoM, we have to do at least 4 breadth subjects with a maximum of 6 which allows the exploration of other subjects in other faculties. This can be used to fulfill the pre-requisites of a post-graduate course that you want to do in another faculty.
TL;DR You should be able to get into any post-graduate course from any degree provided you do the pre-requisite subjects during your undergraduate degree. I'm too tired to know if what I said made any sense but hope it helped somewhat