Are market structures on a spectrum? So I understand that each market structure has their own characteristics, and that for instance Perfect Competition involves high competition, and I believe Monopolistic competition slightly less so, oligopoly even less, and monopoly virtually none.

However, is a market structure pretty much set in stone? Or does the structure change within a spectrum depending on competition for instance?

i.e. Would it be right to say that if competition in a market which was an oligopoly has increased and dominative firms have lost some of their market power, then the market is beginning to resemble that of monopolistic competition and less like an oligopoly?
If there were such a spectrum, it would not be one dimensional. For instance, we could compare the competitiveness of markets with homogeneous products in terms of the number of firms in that market, and have the following spectrum:


monopoly: one firm, no competition
(Cournot) oligopoly: $n$ firms ($n&lt;\infty$), imperfect competition 
perfect competition: infinitely many firms, perfect competition. 


However, this spectrum only works homogeneous products. When you talk about monopolistic competition, i.e. firms competing with differentiated products, then a new dimension opens up: non-price differences in products. An example would be cell phones with different operating systems (e.g. iOS and Android). A small increase in the number Android-powered phone brands is not necessarily going to reduce the market power of iPhones. 

So the spectrum of market competitiveness is not as straightforward as you envisioned. While the two extreme cases, perfect competition and monopoly, are pretty clear, things in between are much less so. For example, a 2-firm Cournot market could be more competitive than a 2-firm monopolistically competitive market, if you carefully choose the demand functions for the latter. So at least in the comparison between oligopoly and monopolistic competition things are not as deterministic as you thought.