立て

連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 立(た)てる (tateru, “to stand (something) up”).

立(た)て • (tate) 

1. a party or banquet

   Synonyms: 宴(えん)会(かい) (enkai), 酒(しゅ)宴(えん) (shuen)

2. treating others to food and/or drink

   Synonym: 奢(おご)り (ogori)

3. the general meaning or gist of something

   Synonyms: 筋(すじ) (suji), 趣(しゅ)旨(し) (shushi)

4. a rule or regulation

   Synonyms: 決(き)まり (kimari), 掟(おきて) (okite)

立(た)て • (tate-) 

1. main, head, central
2. (attaches to verbs) an intensifier

立(た)て • (-tate) 

1. (attaches to verbs in continuative form) just (done)

   生(う)まれたての子猫(こねこ) ― umare-tate no koneko ― newborn kitten

   焼(や)き立(た)てのパン ― yaki-tate no pan ― freshly baked bread

   搗(つ)き立(た)ての餅(もち) ― tsuki-tate no mochi ― fresh mochi

立(た)て • (-tate) 

1. used to count successive defeats

   Synonym: 連(れん)敗(ぱい) (renpai)

As above, with rendaku (連(れん)濁(だく)).

立(だ)て • (-date) 

1. especially
2. attaches to a number of horses/cattle to denote a carriage pulled by that many; similarly for oars on a boat

   二(に)頭(とう)立(だ)ての馬(ば)車(しゃ) ― nitō-date no basha ― a two-horse carriage

立(だ)て • (-date) 

1. used to count movies or plays in a program
2. used to count methods / approaches in a plan