If height is truly the issue here, why not suggest some open pillars between the tiers. It will add a lot of height without adding cake. Filling the space between the tiers with fresh flowers will look beautiful and won’t add extra work on you, apart from the pillar structure.
Otherwise, there’s no way to get more cake without paying for more cake! ;-)
Jenniffer White, Cup a Dee Cakes - http://cupadeecakes.blogspot.com