Yes, blockage is most likely in the outside drains. Lift the covers and the junctions underneath should be empty. If not, rod the drains to clear the blockage(s). Be extra careful as you've been using corrosive chemicals, wear strong rubber gloves and eye-protection. Do NOT use power-washer to clear drains as there is a high risk of unpleasant and possibly dangerous splash back.
Any reason why this toilet in particular is causing problems? Any baby-wipes, face-wipes being flushed? These are advertised as "flushable" but they are not bio-degradable like toilet-paper.