I have purchased 1/2" engineered flooring. My subfloor is 5/8" plywood with 16"oc floor joists. I plan on adding 1/4" or 3/8" plywood on top of my existing subfloor to bring flooring height up to equal existing tiled floors. Would the 5/8 plus 1/4" or 5/8" plus 3/8" subfloor be ok to install the hardwood parallel to the floor joists? Or should I add blocking between my floor joists to beef up the floor. I want to run my hardwood parallel with floor joists because I think it would look better than going perpendicular to joists.

If you are adding the plywood and you stagger the joints of the plywood with the existing subfloor their will be no issues.