We have surveyed a sample of 165 solar-type spectroscopic binaries (SB) with periods from 1 to 30 days for higher-order multiplicity. 62 targets have been observed with the NACO adaptive optics system and 13 new physical tertiary companions were detected. Another 12 new wide companions (5 still tentative) were retrieved from the 2MASS (<II/246>) sky survey. Our binaries belong to 161 stellar systems; of these 64 are triple, 11 quadruple and 7 quintuple. After correction for incomplete detection, the fraction of SBs with additional companions is 63+/-5%. We find that this fraction is a strong function of the SB period P, reaching 96% for P<3d and dropping to 36% for P>12d. Period distributions of SBs with and without tertiaries are significantly different, but their mass ratio distributions are identical. New statistical data on the multiplicity of close SBs indicate that their periods and mass ratios were established very early, but periods of SBs within triples were further shortened by angular momentum exchange with companions.