Hypermethylation of the 7-(mono)methylguanosine (m(7)G) cap structure at the 2' position of the guanosine residue to convert a mono-methylated cap to a 2,2,7-trimethylguanosine cap structure. This type of cap modification occurs on small nuclear RNAs (snRNAs) and small nucleolar RNAs (snoRNAs) and is dependent on prior guanine-N7 methylation.