People have disappointing results from j-poles due to trying to feed them directly with coax. A j-pole is an end fed half wave antenna with the "j" being a matching stub. However, the antenna is a balanced load and must be fed with a balun. I use coaxial baluns made from a half wave length of coax. The feed line will attach a little higher on the stub to allow the 4:1 balun to match 50 ohms. This works (despite many protests on other threads). The response on the antenna will be very flat and it will not interact with other objects.
Unfortunately, even a recent piece in QST magazine perpetuated the myth that j-poles can be fed directly with 50 ohm coax.
As for a multi-band j-pole, there are such things. Arrow Antenna makes 2 meter/440 j-poles. They also make one for 155/460. These are both direct fed from the bottom (an alternate to the balun). However, although I have seen the "copper cactus" design, it will not be very broad band outside its design center frequencies. You might make a slight sacrifice of gain for flat response by using a discone. Antenna gain is always at the cost of bandwidth and radiation angle. High gain broadband antennas like log periodics are directional and expensive.