How does trademark law protect a logo?

Sometimes applicants find solutions (!) to reduce the cost of registration such as GE GENERAL ELECTRIC INNOVATION AT WORK. Instead of proceeding three applications they wish to solve the problem with one application. It reduces the total cost of three registrations but the owner was going to use three factors separately and it may cause a problem. This makes the protective power of the registration weakened. Infringers use the actual usage of the trademark. After registering GE GENERAL ELECTRIC INNOVATION AT WORK, if the owner uses just GE or GENERAL ELECTRIC he makes a differentiation from the registered trademark. If an infringer wants to move closer to the sign and he starts to use GENERALLY ELECTRIC, what shall be done against him? The owner of the trademark additionally needs may be a help from unfair competition law to stand by trademark registration. I always strongly advice to register the trademark as you use it. If there are more than one, then may be the filings will be more. Adding side factors to an application because of different motivations may damage the distinctiveness of the trademark or logo or slogan.