Dear Nicholas, can you provide some pointers to Triple Article Disseration, please? Google only shows me your question, so I am not sure what you mean by this.

The advantage of a triple article dissertation over a monograph is that you break the work down into chunks which all have previous approval of the scientific community. As such it gives you more an idea whether you are on track or not, along the way.

I see two disadvantages to this approach. First, some journals have a very slow acceptance process, so you need the time to await acceptance of a part of your work. Second if your individual articles are too loosely related it might be difficult to write an introduction which convincingly combines the articles into a coherent argument. I have seen some PhD candidates struggle or even fail on this last hurdle.  

I think the benefits of combining published articles into a theses outweigh the costs. 

Assuming TAD is just one form of an article-based thesis, which in many fields/universities would constitute 4 or 5 articles, the advantages also include: 1. Your work can be cited earlier (which helps finding your next job), 2. your will have journal papers in your name when defending your thesis (which helps finding your next job), 3. it helps keeping supervisors more closely involved (which is especially helpful for parttime PhD candidates), 4. It ensures your will have at least some journal papers in case you do not finish your PhD in the end (which sadly does happen, especially with people who work on their PhD other than in a 3 or 4 year (properly) funded project).

elaborating on the drawback Koen mentioned, your work will be peer reviewed by three different journals. peer review will influence the framing of your papers. Even if you planned for the three (or more) to be aligned nicely, after peer review that coherence may be lost. Furthermore, not all studies lend themselves to dividing it in multiple parts, and finalising the first already after a year. If you need 3 years to finalise the actual study, a classical dissertation might be handier, followed by later journal papers. 

Best thing to do is to find some examples of both options (preferably from your own department) and discuss with your and other supervisors in the department their strengths and weaknesses. 

Thank you all that offered your insights and responses to my question about TAD (Triple Article Dissertation) . As you would assume I have done my due diligence and research in this area.  Most recently I was forced into transferring out of the college I was attending due to their decision to close. Thankfully, my ex-college set me and others up with another college to finish our degree if we desired.  I'm full-time now at Trident University International(TUI) and no longer at Jones International University(JIU).  Once again, thank you one and all who offered their opinions and perspectives.  Moving forward, Nick C. Cicchino