I have a question: How do people even have real counteroffers? Do you apply for multiple jobs and two or more happen to make you an offer? How do you manage to get the times to line up so perfectly?
If you're doing it on your own the key is to apply to several places and communicate a lot with each company's internal recruiters. When you start interviewing ask what the whole process is and what the usual timeline is for each step. After each step send a brief thank you message. If they are slower getting back to you on the next step than you expected send a quick message to check on when you can expect to hear from them. As you're going through the process at various companies some will progress faster than others. Make sure that the slower ones are aware you're further along in interviews at other companies so they can catch up. When faster companies propose dates for the next step choose something in the longer end of the range to slow things down. Once you have your first offer inform the other companies you're interested in that you have an offer and they need to start wrapping things up one way or the other.
Most companies can be flexible about their timelines. Even places that are known for long application processes can be significantly sped up if they know you're on a deadline.