The letter I is one of my least favorite. Here are short words containing at least two of them.
HILI IBIS ILIA IMID IMPI INIA INTI IRID IRIS IWIS IXIA KIWI LIRI MIDI MINI MIRI NIDI NISI PIKI PILI TIKI TIPI TITI ZITI
AALII ACINI AIOLI ALIBI AMICI ANIMI BIALI BIFID BIKIE BINDI BINIT BLINI CHILI CILIA CIRRI CIVIC CIVIE CIVIL DIDIE DIGIT DISCI DIXIT FICIN FINIS FIXIT GENII IAMBI ICIER ICILY ICING ICTIC IDIOM IDIOT ILIAC ILIAD ILIAL ILIUM IMIDE IMIDO IMIDS IMINE IMINO IMMIX IMPIS INDIE INDRI INFIX INION INTIS IODIC IODID IODIN IONIC IRIDS IRING ISSEI IVIED IVIES IXIAS JINNI KIBBI KIBEI KILIM KININ KIWIS LIBRI LICHI LICIT LIMBI LIMIT LININ LIPID LIPIN LITAI LIVID MEDII MIDIS MILIA MIMIC MINIM MINIS MITIS NIHIL NIMBI NISEI NITID NIXIE OIDIA ORIBI PIING PIKIS PILEI PILIS PIPIT PIXIE PRIMI RADII RICIN RIGID RISHI SIGIL TEIID TIBIA TIKIS TIMID TIPIS TITIS TORII VIGIL VILLI VINIC VIRID VISIT VIVID VIZIR ZITIS ZIZIT