No, you will not need a second EU Visa to other Schengen areas. Suppose a Schengen state has already issued you an extended stay visa or residence permit. In that case, you may travel anywhere within the Schengen area, as long as you respect the maximum duration. This length of time is typically known as “short stays” and lasts 90 days within 180 days.
You may still freely travel within the Schengen area within this time frame.
Traveling within the Schengen Area
Passport or another form of travel authorization. If you want to travel, you must always have a valid passport or another travel document. Your passport or travel document must have been issued within ten years. Your passport or travel document is valid for three months after leaving the Schengen area.
Traveling with a short-term visa
You can only enter the Schengen area once if you have a valid Schengen single entry visa. Every 180 days, you are allowed to stay in the Schengen area for 90 days. You can travel to and remain in any Schengen country during these 90 days. Are you passing via another nation on your way to the Schengen area? Then you must demonstrate that the Netherlands is the intended destination.
Do you have a valid multiple entry visa that allows you to travel on several occasions?
Multiple entries and exits are permitted inside the Schengen area. Initially entering the Schengen area, you must declare your primary destination.
Do you require a visa?
During the visa-free access period, you can stay in the Schengen area for up to 90 days or 180 days. You are also permitted to enter and exit the Schengen area.
A valid residence permit / national visa allows you to travel between the Schengen countries.
You can stay in any Schengen country for up to 90 days every 180 days if you have a valid residency or Schengen visa.