Guide to becoming a network admin

I am currently a network/pc technician pulling double duty as a help desk administrator. I am getting some exposure to the network admin side but not enough to be a full network admin yet..Does the Jr. Admin title still exist and if so, with my Bachelors, Associates, CCNA, Network+ A+ degrees/certifications and 3 years IT experience, how can I get my foot in the door on the network admin side in another company since my current job does not allow for alot of growth into that area. Can anyone tell me how they did it and offer any suggestions? Will a company be will to take someone like myself under their wing and get me into the program or will they demand I jump right out of the gate into their environment?

Rich