put up with=stand/bear 忍受
put on with应该是没有这个词组的,我记忆中没有,网上也差不到.put on上演,穿上,张贴（海报）
keep up with =catch up with赶上,这两个的区别在于keep up with,追赶人与被追赶人所处情况差不多,而catch up with暗示追赶人处于落后地位.