I created a Site-to-Site VPN Connection by following the provided steps: https://learn.microsoft.com/en-us/azure/vpn-gateway/vpn-gateway-howto-site-to-site-resource-manager-portal
If I wish to create another Site-to-site VPN connection (to another site using a different Local Network Gateway) can I do so using the same Virtual Network Gateway? or do I need to create an additional Virtual Network Gateway?
You do not need a new VPN Gateway in Azure to create multiple connections to your Vnet. Simply create a new Local Network Gateway for your second site, and add a connection between the existing VPN Gateway and the new Local Network Gateway.
See doc here for more details and process: https://learn.microsoft.com/en-us/azure/vpn-gateway/vpn-gateway-howto-multi-site-to-site-resource-manager-portal