Changing ulimit on Amazon EC2

Is there a way to increase the ulimit -n (open files) for an Amazon EC2 instance? I am running an amazon m3.2xlarge ubuntu instance for testing purposes. The ulimit -Hn is 4096 but I need over 10k. I have even tried temporarily getting higher instance types but no luck.

I have googled around for quite a while but there are only topics on this that are a few years old. Most suggest changing the limits.conf file found in /etc/security/limits.conf but the limit is read only so I cannot change permissions.

Are there any alternative ways to change this ?

Edit - my etc/security/limits.conf file

#*               soft    core            0
#root            hard    core            100000
root            soft    nofile          16500
root            hard    nofile          16500
#*               hard    rss             10000
#@student        hard    nproc           20
#@faculty        soft    nproc           20
#@faculty        hard    nproc           50
#ftp             hard    nproc           0
#ftp             -       chroot          /ftp
#@student        -       maxlogins       4

If you set up the instance or you have sudo privileges, you can change those configuration files. Just prepend your command to open the file with sudo, (example sudo vi /etc/security/limits.conf).