Putting in an additional engine means a complete redesign of the aircraft (the weight distribution, wings, air intakes, flight control software etc), it can be done but it won't be Tejas/LCA anymore - essentially it's moving towards AMCA.
GE 404 was the original engine (built for F18); it went on to become quite popular as about 1000+ F18s were built. Since Tejas project started in the late 80s/early 90s, 404 engine was chosen. GE came up with 414 much later (as an improvement for F18s again). The Tejas project kept chugging along with 404 in their design (414 being slightly larger in diameter didn't lend itself to a simple plug-n-play into Tejas design). Kaveri project never really came out of it's gestation period through the design phase of Tejas.
Indian Navy (late entrant to the project) wanted a higher thrust engine; and hence 414 became an option but still required some redesign. When Air Force noted the rework (and as they were unhappy with 404 on Tejas) they piled onto Mk2 version. But of course Mk2 was taking forever to come through as ADA wanted to get all the carrier features into the design (which effort they had totally underestimated as they had little a priori knowledge of carrier operations). Unable to wait for airforce Mk2 to come through IAF and HAL did an interim jugaad of Tejas Mk1A (with 404 engine itself).
Essentially the whole project was mismanaged. If right decisions were taken at the right time we would probably have had several squadrons of Tejas flying by now. But all is not lost!! Tejas Mk1A with very modern avionics will be a reasonably good fighter.
Buying military equipment is like buying an insurance policy; when you don't have it you're sweating all the time because you're not prepared for a bad eventuality. But once you get it, you don't care about the 'risky' duration you put yourself through (and maybe even happy that you saved money during that phase
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