What English verb has the most possible complements?

Assuming you mean verb complements (i.e., not "sign post"), here is a
list of all I can find with five or more (not counting complements
that are homographs):

16 go: go about [vi] go along [vi] go around [vi] go by [vi] go down [vi] go in [vi] go off [vi] go on [vi] go out [vi] go over [vi] go round [vi] go through [vi] go to [vi] go under [vi] go up [vi] go without [vi]
16 get: get about [vi] get across [vi] get along [vi] get around [vi] get away [vi] get back [vi] get by [vi] get down [vi] get in [vi] get off [vi] get on [vt] get out [vi] get over [vi] get round [vb] get through [vi] get up [vi]
16 come: come about [vi] come across [vi] come along [vi] come around [vi] come back [vi] come by [vi] come down [vi] come in [vi] come off [vi] come on [vi] come out [vi] come over [vi] come round [vi] come through [vi] come to [vi] come up [vi]
15 put: put about [vi] put across [vt] put away [vt] put by [vt] put down [vb] put down [vt] put in [vb] put off [vb] put on [vb] put out [vb] put over [vt] put through [vt] put to [vb] put together [vt] put up [vb]
15 turn: turn about [vb] turn around [vb] turn away [vt] turn back [vi] turn down [vi] turn in [vt] turn off [vi] turn off [vt] turn on [vt] turn out [vt] turn over [vt] turn round [vb] turn to [vi] turn under [vt] turn up [vt]
13 lay: lay about [vi] lay aside [vt] lay away [vt] lay by [vt] lay down [vt] lay in [vt] lay low [vt] lay off [vt] lay on [vt] lay out [vt] lay over [vt] lay to [vt] lay up [vt]
11 knock: knock about [vt] knock around [vt] knock back [vt] knock down [vt] knock off [vi] knock off [vt] knock on [vt] knock out [vt] knock over [vt] knock under [vi] knock up [vt]
11 take: take about [vt] take away [vb] take back [vt] take down [vb] take in [vb] take off [vb] take off [vi] take on [vb] take out [vb] take over [vt] take up [vb]
11 send: send away [vt] send back [vt] send down [vt] send forth [vt] send in [vt] send off [vt] send on [vt] send out [vt] send over [vt] send round [vt] send up [vt]
11 run: run along [vi] run around [vi] run away [vi] run down [vt] run in [vt] run off [vt] run on [vi] run out [vi] run over [vi] run through [vt] run up [vi]
11 hold: hold away [vi] hold back [vb] hold down [vb] hold forth [vb] hold in [vb] hold off [vb] hold on [vi] hold out [vb] hold over [vb] hold together [vt] hold up [vb]
10 throw: throw about [vi] throw away [vt] throw back [vt] throw by [vt] throw down [vt] throw in [vt] throw off [vt] throw out [vt] throw over [vt] throw up [vb]
10 pull: pull away [vi] pull down [vt] pull in [vt] pull off [vt] pull out [vi] pull over [vi] pull round [vt] pull through [vt] pull together [vi] pull up [vt]
10 lie: lie along [vi] lie athwart [vi] lie back [vi] lie by [vi] lie down [vi] lie in [vi] lie off [vi] lie over [vi] lie to [vi] lie up [vi]
10 cast: cast about [vt] cast around [vi] cast away [vt] cast back [vt] cast behind [vt] cast down [vt] cast off [vt] cast on [vt] cast out [vt] cast up [vt]
10 bring: bring about [vt] bring down [vt] bring forth [vt] bring forward [vt] bring in [vt] bring off [vt] bring on [vt] bring out [vt] bring to [vt] bring up [vt]
9 sit: sit around [vi] sit back [vi] sit by [vi] sit down [vi] sit in [vi] sit out [vt] sit over [vi] sit through [vt] sit up [vi]
9 set: set back [vt] set by [vt] set down [vt] set in [vt] set off [vt] set on [vt] set out [vt] set to [vi] set up [vt]
9 hang: hang around [vi] hang back [vi] hang behind [vi] hang off [vi] hang on [vi] hang out [vi] hang over [vi] hang together [vi] hang up [vt]
9 give: give away [vb] give back [vi] give down [vt] give in [vt] give off [vt] give on [vi] give out [vb] give over [vb] give up [vb]
9 fall: fall away [vi] fall back [vi] fall down [vi] fall in [vi] fall off [vi] fall out [vi] fall over [vi] fall to [vi] fall together [vi]
8 talk: talk around [vt] talk away [vt] talk back [vi] talk down [vt] talk in [vt] talk out [vt] talk over [vt] talk up [vt]
8 stand: stand by [vi] stand down [vi] stand in [vt] stand off [vi] stand on [vi] stand out [vi] stand over [vi] stand up [vb]
8 look: look around [vi] look back [vi] look down [vb] look in [vi] look on [vi] look out [vb] look over [vt] look up [vb]
8 kick: kick around [vt] kick back [vi] kick in [vt] kick off [vi] kick out [vi] kick over [vi] kick through [vi] kick up [vt]
8 keep: keep away [vi] keep back [vt] keep down [vt] keep in [vt] keep off [vt] keep out [vt] keep under [vt] keep up [vt]
8 carry: carry away [vt] carry back [vt] carry forward [vt] carry off [vt] carry on [vt] carry out [vt] carry over [vt] carry through [vt]
8 belly: belly bump [vi] belly bunt [vi] belly bust [vi] belly dance [vi] belly flop [vi] belly gut [vi] belly in [vi] belly whop [vi]
8 let: let bug [vi] let dab [vi] let down [vt] let in [vt] let off [vt] let on [vi] let out [vt] let up [vi]
8 break: break away [vt] break back [vi] break even [vi] break in on [vt] break in upon [vt] break into [vt] break off [vi] break out [vi]
7 walk: walk back [vi] walk down [vt] walk off [vt] walk on [vi] walk out [vi] walk over [vi] walk up [vt]
7 do: do away [vt] do down [vt] do for [vt] do in [vt] do up [vt] do with [vt] do without [vt]
7 cut: cut across [vt] cut back [vt] cut down [vt] cut on [vt] cut over [vt] cut round [vi] cut under [vt]
7 call: call down [vt] call forth [vt] call in [vb] call in [vt] call off [vt] call out [vt] call up [vt]
7 blow: blow away [vt] blow down [vt] blow in [vi] blow off [vi] blow out [vi] blow over [vi] blow up [vt]
7 beat: beat about [vi] beat back [vt] beat down [vt] beat off [vb] beat off [vt] beat out [vt] beat up [vi]
6 strike: strike back [vi] strike below [vt] strike in [vi] strike off [vt] strike out [vt] strike up [vi]
6 shut: shut away [vt] shut down [vi] shut in [vt] shut off [vt] shut out [vt] shut up [vb]
6 play: play back [vi] play forward [vi] play off [vt] play on [vi] play out [vt] play up [vi]
6 pass: pass away [vb] pass by [vt] pass off [vt] pass out [vi] pass over [vt] pass up [vt]
6 make: make down [vi] make off [vi] make out [vi] make out [vt] make over [vt] make up [vt]
6 hand: hand down [vt] hand in [vt] hand off [vt] hand on [vt] hand out [vt] hand over [vt]
6 draw: draw away [vt] draw back [vt] draw down [vt] draw in [vt] draw into [vt] draw out [vt]
6 close: close down [vi] close in [vb] close off [vt] close out [vt] close up [vb] close with [vt]
6 back: back away [vi] back down [vi] back in [vi] back off [vt] back out [vi] back up [vi]
5 write: write down [vt] write in [vt] write off [vt] write out [vt] write up [vt]
5 trade: trade down [vi] trade in [vt] trade name [vt] trade off [vi] trade up [vi]
5 tear: tear around [vi] tear away [vt] tear down [vt] tear off [vt] tear up [vt]
5 stick: stick around [vi] stick off [vb] stick on [vi] stick out [vi] stick up [vi]
5 step: step back [vi] step down [vt] step in [vi] step out [vi] step up [vt]
5 sign: sign in [vi] sign off [vi] sign on [vi] sign out [vi] sign up [vi]
5 rub: rub down [vt] rub in [vt] rub off [vi] rub out [vt] rub up [vt]
5 round: round in [vt] round off [vt] round out [vb] round to [vi] round up [vb]
5 roll: roll back [vt] roll in [vi] roll out [vi] roll over [vt] roll up [vt]
5 pick: pick in [vt] pick off [vt] pick out [vt] pick over [vt] pick up [vb]
5 check: check in [vi] check off [vt] check out [vi] check over [vt] check up [vb]
5 buy: buy in [vt] buy into [vt] buy off [vt] buy out [vt] buy up [vt]
5 work: work in [vt] work off [vt] work out [vt] work over [vt] work up [vb]

[ Editor: the reply was posted unsigned from Questrel, Inc. ]