There are some enhancement tech choices that generally allow you to pick 1 of 3 choices, such as some % more powerful, some % cheaper to build or some % smaller for ship components. You aren't allowed to later research the other two. However, that does not mean you can't get the other two! The short answer as to how is to farm additional tech enhancement choices to supplement the one you made and researched to other civs through careful tech trading (this only works, of course, if you haven't disabled tech trading -- if you have, this entire post is moot for you).
A lot of players quickly realize you can trade for those techs from other civs. However, not all of those realize you can use this for a bit of an exploit: Very carefully assess what techs the AI has. Do not offer them any of your enhancement techs unless they have already researched one of the other two choices for that enhancement tech -- as an example, if you researched Armor Miniaturization, do not trade Armor Miniaturization to any civilization that has not already researched Low-Cost Armor or Reinforced Armor (the other two tech choices for "Armor Optimization"). Do trade them Armor Systems (the parent tech that leads to Armor Optimization) if they don't already have it ... that way, they should eventually research Low-Cost Armor or Reinforced Armor, which means you can then trade for one of those and have two enhancement techs! There's no guarantee when they'll research Armor Optimization (they might put it off for a long while if they're focused on other techs), or if so that they'll pick Low-Cost Armor or Reinforced Armor (they might instead research Armor Miniaturization themselves) ... and likewise with a second rival civilization -- its rather unlikely, in fact, that of 3 civs (yourself and two rivals) you'll be able to get all 3 enhancement choices for each tech, so expand your 'farming' enhancement choices to as many civs as possible, and don't forget minor civs.
Unfortunately, minor civs seem to hit a tech ceiling ... I don't know if they stop researching altogether, but even Age of Expansion techs they seem to stop researching after awhile. However, they do research some and I think its worth farming out at least low level techs. Armor Optimization choices affect every kinetic armor tech, even the higher level ones.
To really keep an edge, you might want to keep all the enhancement techs you reap to yourself -- even the one you actually research. At least, you might want to consider not trading the enhancement techs to non-allies so that you'll exclusively have multiple enhancements.
