You can invite influencers to your campaign both when it is in draft mode or when it is running. You can also add more influencers until the campaign has ended. Please make sure there is enough time for them to accept the invitation.
Go to the influencers tab and see the whole list of available influencers.
Choose the campaign from the drop-down list on the right side of the screen and click Apply. 

For all kinds of campaigns (draft public, running public/private) search results will get adjusted as per campaign settings - channels, category, reach, etc. So you will get influencers that match the settings you have applied to your campaign. You can always reset the filter and search for any influencer but in this case, there might be a slight adjustment needed on the campaign. Like adding more social media channels where the content should be posted.

If you are adding participants to the drafted Private campaign then you will be redirected to the Select Influencers page of the Campaign creation wizard. 

Once you added influencers to the basket of campaign #1 (for example) and need to switch to another campaign #2 you still can switch how much you need and won't lose the progress on any step. But to invite influencers you would need to get back there, of course. 

It is also possible to add influencers right from the Campaign.