I did my ATPL exams while working full time however my employer allowed me to do a condensed 4 day week. I then dropped down to a 3 day week and did CPLMEIR training on my days off. It wasn't ideal but I made it work, I imagine it's definitely doable alongside a 5 day working week but much less practical and could cost more since lessons risk being very spread out.
Are you in Scotland btw? There is only really 1 option up here in ACS at the moment.