Is the 80% tile flooring down now vinyl or ceramic?
Is the laminated flooring a free floating style, or a glued version, or a just how is it to be laid.
What I would do is to floor the remaining 20% so that your floor is level. Then consider the style of lam flooring and seek your options. You can just lay down that plastic foam underlayment and then put your lam over that. you will raise the level of the flooring about 3/4 of an inch with the tile and the foam and the lam. So, be sure you can go with this height around the cabinets, thresholds, and other areas.
Come back with more details and we can surely assist you with more specific answers.