Yes you'll always get algae.
BUT - more filtration as you suggest will not get rid of your problem. Lets start from scratch.
ammonia ->nitrite ->nitrate - this happens in aerobic conditions. This is what your filtration does. Where does this nitrate go - algae, or removed by water changes. Your exernal filter, like a wet/dry, or a UGF is a tremendous nitrate producing machine, and the end result of excess nitrates is lots and lots algae. If that's the filtration you have, you can only get the nitrate out with water changes. These big biofilters build a lot of nitrate quickly, and if you don't clean gunk out frequently,( and with big fish loads that can mean every day or 2!) you will hit these problems.
You can get nitrate out of your system by 'denitrafication' - this only happens though in anoxic conditions. You can do this with a commercial denitrafier from aqua medic or whoever, however these are costly and tricky to run. You can also rely on the anoxic properties of a plenum system , or a deep sand bed.
You can also use preferred types of macroalgae to suck out the nitrate, in preference to pest algaes. These are commonly kept in a sump or refugium.
Extensive use of live rock is also a possible fix. The outer layers of the rock will render ammonia to nitrate, while deeper into the rock anoxic conditions prevail and nitrate is reduced to nitrogen gas. This can work IF you have lots of live rock, as it's not a etrribly efficient way to denitrafy. If you have lots of fish, and an external or wet/dry, the live rock will likely be overwhelmed with nitrate.
So for you, I tihnk you need to reexamine your filtration philosophy, and do a bunch of water changes and get a clean up crew because a big wet dry or whatever will not eliminate your problems.
I don't know , or much care what your nitrate test kit says because 1. they're horribly inaccurate, and 2. most nitrate is being fixed quickly by the algae so won't show. And we haven't even mentioned trying to remove phosphate , though that may well be worthwhile.