Reviewing through your inquiry, yes, there is a limit of 3 custom navbar items. For example:
That being said, if you are interested in developing an adv custom theme for your instance it should be possible to add in additional nav bar items. If you are interested in pursuing an adv custom theme there are a couple of options I would recommend:
1. If you are wanting to develop this yourself I would suggest reaching out to the Jive Developers space here in the Jive Community, where you can collaborate with other developers on potential custom options you are interested in for your instance.
2. If you would like assistance developing a custom theme for your instance our Professional Services team can work with you to determine the scope of the project and help develop a custom theme which meets your use case. If you are wanting to pursue this option, please either reach out to your account manager, or submit a case in your customer group here in the Jive Community and the next available member of our support team can get an engagement started for you.