We have surveyed a sample of 165 solar-type spectroscopic binaries (SB) with periods from 1 to 30 days for higher-order multiplicity. A subsample of 62 targets were observed with the NACO adaptive optics system and 13 new physical tertiary companions were detected. An additional 12 new wide companions (5 still tentative) were found using the 2MASS all-sky survey. The binaries belong to 161 stellar systems; of these 64 are triple, 11 quadruple and 7 quintuple. After correction for incompleteness, the fraction of SBs with additional companions is found to be 63% ± 5%. We find that this fraction is a strong function of the SB period P, reaching 96% for $P<3^{\rm d}$ and dropping to 34% for $P>12^{\rm d}$. Period distributions of SBs with and without tertiaries are significantly different, but their mass ratio distributions are identical. The statistical data on the multiplicity of close SBs presented in this paper indicates that the periods and mass ratios of SBs were established very early, but the periods of SB systems with triples were further shortened by angular momentum exchange with companions.