The effects of tagging protonated glycine with either He or with between 1 and 14 H2 molecules on the infrared photodissociation (IRPD) spectra and the ion structure was investigated. Differences in the IR spectra with either a single He atom or H2 molecule attached indicate that even a single H2 molecule can affect the frequencies of some vibrational bands of this simple ion. The protonation site is the preferred location of the tag with He and with up to two H2 molecules, but evidence for H2 attachment to the hydrogen atom of the uncharged carboxylic acid is observed for ions tagged with three or more H2 molecules. This results in a 55 cm-1 red shift in the carboxylic acid OH stretch, and evidence for some structural isomers where the hydrogen bond between the protonated nitrogen and the carbonyl oxygen is partially broken as a result H2 molecules attached to this site is observed. These results are supported by theory, which indicates that H2 molecules can effectively break this weak hydrogen bond with three or more H2 molecules. These results indicate that large spectral shifts as a result of H2 molecules attaching to sites remote from the charge can occur and affect stretching frequencies as a result of charge transfer, and that tagging with multiple H2 molecules can change the structure of the ion itself.