  Using a volume-limited sample of 550 groups from the Galaxy And Mass Assembly
(GAMA) Galaxy Group Catalogue spanning the halo mass range $12.8 < \log
[M_{h}/M] < 14.2$, we investigate the merging potential of central Brightest
Group Galaxies (BGGs). We use spectroscopically-confirmed close-companion
galaxies as an indication of the potential stellar mass build-up of
low-redshift BGGs, $z \leq 0.2$. We identify 17 close-companion galaxies with
projected separations $r_{p} < 30$ kpc, relative velocities $\Delta v \leq 300$
km s$^{-1}$, and stellar-mass ratios $M_{BGG}/M_{CC} \leq 4$ relative to the
BGG. These close-companion galaxies yield a total pair fraction of $0.03 \pm
0.01$. Overall, we find that BGGs in our sample have the potential to grow in
stellar mass due to mergers by $2.2 \pm 1.5\%$ Gyr$^{-1}$. This is lower than
the stellar mass growth predicted by current galaxy evolution models.
