The best replacement for basecamp is sharepoint.

The best alternatives to basecamp are rated as following:
★★★★★  sharepoint
★★★★★  mapsource
★★★★★  asana
★★★★  jira
★★★  trello
★★★  podio
★★  assembla
★★  smartsheet
★★  backpack
★★  teamworkpm
★★  teamwork
★★  salesforce
★★  wrike
★  huddle
★  microsoft project
★  zoho
★  redmine
★  evernote
★  activecollab
★  manymoon
★  highrise
★  google docs
★  confluence
★  redbooth
★  pivotal tracker
★  teambox
★  intervals
  goplan
  flow
  pivotal
  central desktop
  ms project
  campfire
  fogbugz
  clarizen
  lighthouse
  slack
  5pm
  base camp
  google wave
  daylite
  workamajig

Your alternative for basecamp is not listed? Suggest!
Speaking about basecamp, one probably shouldn't forget about google docs.

Other search terms related to basecamp and their ratings are:
★★★★★ google docs
★★★ github
★★★ campfire
★★ highrise
★ freshbooks
omnifocus
agile
You have in mind a companion for basecamp and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of basecamp in all years. Click on graph for more.
basecamp
sharepoint
mapsource