You could but there are time and budget issues. If you do both sets of exams at the same time (study once for both) you then have to pass both flight tests within the following 36 months which with the associated training will cost a lot. You'll also only need one of those licences for your first job, so you're paying extra for a licence you don't need and may never use. On the other hand, If you only get one licence (and a job) then once you hit the minimum flight hours you you could get both ATPLs issued at the same time with one sim check paid for by your company. The irony is that converting a CPL/IR costs a fortune but converting an ATPL is the cheapest and easiest conversion you'll ever do. Personally in that situation I would get both medicals and take both sets of exams simultaneously. Its minimum investment and effort (a couple of thousand). Then I would spend 3 months to get one licence and spend 9 months trying to get a job. At the end of that if I felt I needed the other licence I would still have 2 years remaining on the exams to develop a plan B. You may even find having a UK licence with EASA ATPL credits on your CV useful (or vice versa).