It is difficult to find someone with your same level fitness and speed in one sport let alone three sports so if you are going to train with a partner it may require a different person for each sport. An ideal arrangement is one in which you will play off of each other's strengths. Take cycling for example. If your strength is climbing but you lack power on the flats then an ideal partner would be someone who would make you work to keep up with them on the flats as long as you are able to stay within your individual heart rate training zone. That is to say, if you are pushing your lactate threshold just to keep up then you are probably working too hard, which brings me to my next point. If you are going to train with a partner you need to have similar objectives for that particular workout or have an understanding of what your partners intentions are if you're tagging along.
If your training plan for the day is to ride 90 minutes with 20 minutes at race pace but your partner plans on doing 30 minutes warm up and then 60 minutes of all out, then someone's plan is going to take a back seat and you may end up going much harder than you intended that day which may sabotage training later that day or the next day. In my personal experience it seems that this issue is the one I run into the most when training with someone, people seem to be afraid to go easy... it has to be all out, all the time (a topic for a future post) or it turns into a competition, again, sabotaging your training plans for that day.
Another key point in training with someone is that you need to have a back up plan in case they have to cancel. If you are tied to someone else's schedule you may end up missing a lot of training due to the fact that you are planning around their availability. As you are waiting for them to get home from work the weather may take a turn for the worse and you will be kicking yourself that you didn't ride two hours ago when it was sunny and windless.
In the end, if you are going to train with someone, choose your partners wisely. It should be a symbiotic relationship in which you have similar goals and are aware of what the training plan is for that day. The important thing is that you don't miss out on fulfilling your goals because you were training at somebody else's pace. Remember, their zone 2 may be your zone 3 or vice versa. Training with someone is fun but don't forget who's goals you are training for.