Balancing transactions on a single connection to different pools

While in theory this is possible, doing it for something other than HTTP will be much more difficult since HTTP already has a profile on the LTM to parse the payload very efficiently. To do it with a different protocol you are going to have to parse the TCP payload yourself via CLIENT_DATA event and you will have to use a oneconnect profile which may or many not work with your protocol https://support.f5.com/kb/en-us/solutions/public/7000/200/sol7208.html and https://devcentral.f5.com/wiki/iRules.CLIENT_DATA.ashx. If your key is very early in the payload and is consistent you can probably get away with only collecting a small amount of the payload.