The product is a vitamin supplement system which includes several different supplements, but didn't want to TM "Galax-y System" as we will want to use "Galax-y" as well on it's own and with other quanitfiers such as "Galax-y Method" or "Galax-y solution", etc************** But our first product says "The Galax-y System" on it, rather than just "Galax-y" which was what we Trademarked.
If your trademark is, in fact, a made up word unique to you alone, adding other words before or after your trademark should not affect its strength.
Strong marks are provided the most protection under trademark laws. These strong marks include words that are used in unexpected ways (e.g., arbitrary uses like Arrow for shirts, Penguin for books) and made up words (e.g., Google, Kodak).
Words like "system" and "method" are generic words that on their own or with other trademarks can be used by anyone. Unless used in an arbitrary way (e.g., "Method" used as a clothing brand), the words must be disclaimed.
A personal review by an IP professional in your area is always a good idea.