By this I mean, is it possible or advisable to change my rhythm so that I wake up on Monday morning, sleep Tuesday afternoon (I'm awake for over 24 hours) and then sleep for over 16 hours till the Wednesday morning. Can we alter our body clock this way?
A few studies have been published concerning this topic.
For example this one: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1330995/
To my knowledge they all had somewhat similar results:
Seven solitary subjects, and two groups of four, spent from 5 to 13 days in an isolation unit without knowledge of time. Three solitary subjects and one group of four adopted fairly regular activity habits with a period of 25-27 h; one subject adopted a period of 30 h, and one of 27 h initially, decreasing to 24-25 h after a few days. One group of four awoke roughly every 24 h, after a sleep which was alternately about 8 h, or about 4 h and believed by the subjects to be an afternoon siesta. Two solitary subjects alternated sleeps of about 8 or 16 h, separated by 24 h of activity.
So while your 'optimal' rhythm might be somewhere around 25 hours of activity in one circadian cycle, there are severe social implications to consider living in 'another timezone' than everybody else in your community.
Concerning the second part of your question and then sleep for over 16 hours, there are studies, which show that for an average adult the optimal amout of sleep lies between 7-9 hours. However, the test subjects in these studies are usually just awake for around 15 hours. So, I do not think that anybody can give you a responsible advice on this matter.
Also, to my knowledge, there is no reasonable amount of evidence for long-term effects such a changed circadian cycle might have on one's health.