Yepp, that is why Multi-Install is the prefered method and Normal-Install is there for choice&compatibility to MCs, which might have a problem with multi-install.
Another thing to mention,...
It seems you want to do the game-swap-trick again, to install it for your friends,...
That is not needed. Once you are able to run Homebrew (for example with your own FMCB'ed MC), you do not need to swap discs, or use discs at all to install it to other MCs...
PS2 V7/DMS3 V2 (FW:2.4b7); Seagate Baracuda 200GB
PS2 V7/CC1.0 (FW:34 hacked v2 BM:2.1.6); Maxtor DiamondMAX9 PLUS 160GB
PS2 SCPH-30004R; NoMod+NoLaser
3xSony MC 8MB
MAX/Datel 16MB with Boot-CD
Custom FMCB 1.8b+ Beta-Build, my AIO 0.5, Sony&xRhino-Linux