On the initial supposition that the core is highly specialized, presumably expensive and is clearly sizeable. Add the fact that what you see in Engineering is only a small part of the overall warp drive system. Note the Warp Nacelles on the outside og most Federation Starships. It is likely you could argue that the warp field of one core would require the second core to be offline in order to operate properly. If the multiple cores were to operate connected to the same Nacelles (i.e. we don't need a separate set of nacelles for the second core) then the complexity arises of preventing a breach of one core's system from bleeding into the second core, efectively destroying the second core.
In this context by breach of the system, I do not mean breach of the core its self, but of the plasma conduits, energy transfer systems, and connections to the nacelles themselves.
On the flip side, if you make the two cores completely independent of each other (no crossover, except perhaps the stored fuel sources; then you would add even more additiona conduits, relays and, yes, even nacelles. If the warp dore and nacelles are a very large portion of the total cost or resource requirements of the vessel, then you could have, for example, possibly three Galaxy Class starships as designed for the equivilent cost/resources of perhaps 1.5-2 Galaxy class starships operating with a reserve Warp Core. And three starships means presence in three places at once.
If a secondary warp core would be installed, I would imagine it would likely be a smaller, more 'emergency use' type which likely would have neither the range nor speed of the main warp core. (Like an emergency generator for when the power goes out, or a 'small' spare tire. etc.)