Context. The multiplicity fraction of stars, down to the substellar regime, is a parameter of fundamental importance for stellar formation, evolution, and planetology. The census of multiple stars in the solar neighborhood is however incomplete. Aims. Our study is aimed at detecting companions of HIPPARCOS catalog stars from the proper motion anomaly (PMa) they induce on their host star, namely, the difference between their long-term HIPPARCOS-Gaia and short-term Gaia proper motion vectors. We also aim to detect resolved, gravitationally bound companions of the HIPPARCOS catalog stars (117 955 stars) and of the Gaia EDR3 stars closer than 100 pc (542 232 stars). Methods. Using the HIPPARCOS and EDR3 data, we revised the PMa catalog for the HIPPARCOS stars. In order to identify gravitationally bound visual companions of our sample, we searched the Gaia EDR3 catalog for common proper-motion (CPM) candidates. Results. The detection of tangential velocity anomalies with a median accuracy of σ(Δv_T) = 26 cm s⁻¹ per parsec of distance is demonstrated with the EDR3. This improvement by a factor 2.5 in accuracy, as compared to Gaia DR2, results in PMa detection limits on companions that are well into the planetary mass regime for many targets. We identify 37 515 HIPPARCOS stars presenting a PMa at significant level (S/N > 3), namely, a fraction of 32% (compared to 30% for the DR2) and 12 914 (11%) hosting CPM bound candidate companions. After including the Gaia EDR3 renormalised unit weight error (RUWE > 1.4) as an additional indicator, 50 720 stars of the HIPPARCOS catalog (43%) exhibit at least one signal of binarity. Among the Gaia EDR3 stars located within 100 pc, we find CPM bound candidate companions for 39 490 stars (7.3% of the sample). Conclusions. The search for companions using a combination of the PMa, CPM, and RUWE indicators significantly improves the exhaustivity of the multiplicity survey. The detection of CPM companions of very bright stars (heavily saturated on the Gaia detectors) that are classical benchmark objects for stellar physics provides a useful proxy for estimating their distance with a higher accuracy than with HIPPARCOS.