Especially while working under time pressure, you can only take care of a few stakeholders. In such cases, you could use a visual classification by interest and influence instead of a stakeholder table. Such a classification can be done very informally by gathering the team around a flipchart and put the outcome into the documentation as needed.
- High impact, great interest: you should involve these people intensively and/or take care of them. Do everything to satisfy this category of stakeholders in all respects. Communication pro-actively with them.
- High impact, low interest: invest just as much effort as needed to satisfy these stakeholders
- Low impact, high interest: these stakeholders can be very helpful for the work on the system: involve them actively and keep them appropriately informed. They can particularly provide feedback on all types of technical or domain details.
- Little effect, low interest: here you could minimize your effort and only provide the information these stakeholders would consume when necessary
Ideally, you have a stakeholder table plus such a classification.
Note: some stakeholders might assess their own influence / power higher than you reflect it in your classification. Publishing this matrix could therefore lead to some frustration among your stakeholders. In case of doubt, keep it private.