Here is my nginx detail:
# nginx -V
nginx: nginx version: nginx/1.0.5
nginx: TLS SNI support enabled
nginx: configure arguments: --prefix=/etc/nginx --conf-path=/etc/nginx/nginx.conf --error-log-path=/var/log/nginx/error.log --http-client-body-temp-path=/var/lib/nginx/body --http-fastcgi-temp-path=/var/lib/nginx/fastcgi --http-log-path=/var/log/nginx/access.log --http-proxy-temp-path=/var/lib/nginx/proxy --http-scgi-temp-path=/var/lib/nginx/scgi --http-uwsgi-temp-path=/var/lib/nginx/uwsgi --lock-path=/var/lock/nginx.lock --pid-path=/var/run/nginx.pid --with-debug --with-http_addition_module --with-http_dav_module --with-http_geoip_module --with-http_gzip_static_module --with-http_image_filter_module --with-http_realip_module --with-http_stub_status_module --with-http_ssl_module --with-http_sub_module --with-http_xslt_module --with-ipv6 --with-sha1=/usr/include/openssl --with-md5=/usr/include/openssl --with-mail --with-mail_ssl_module --add-module=/build/buildd/nginx-1.0.5/debian/modules/nginx-echo --add-module=/build/buildd/nginx-1.0.5/debian/modules/nginx-upstream-fair

This doc says that it should be possible to share the same IP address. I use latest browsers. I intend to have multiple server sections in the config, each for a different app. I am using a self-signed certificate. Anything special needs to be done to the cert?