There's no tower bell ringing at the moment, and handbell ringing is almost entirely limited to people who have a band living in the same house (apart from some experiments with remote online ringing). The Pipes have rung a peal of Stedman Triples, and the Perrinses have rung one of spliced surprise major, but most of the performances on BellBoard these days are minimus.
What can you ring on four? There are 11 plain minimus methods whose plain course is an extent of 24 changes. Instead of showing lines, I will give links to CompLib. The methods are Plain Bob, Reverse Bob, Double Bob, Canterbury, Reverse Canterbury, Double Canterbury, St Nicholas, Reverse St Nicholas, Single Court, Reverse Court and Double Court. (I'm not absolutely sure of my ground here, but I seem to remember that 11 is the magic number).
A surprising number of minimus methods have been rung and named, but I will focus on some traditional well-known four-bell versions of standard methods.
Kent Treble Bob and Oxford Treble Bob each have a plain course of 48 changes, which contains every change twice. The methods are recognisable from their familiar structure, and Oxford turns out to be a double method.
Another old favourite is Bristol Minimus, which now seems to be called Demi-Bristol Alliance. This is based on three bobbed leads of Bristol Major, in which 2, 3 and 4 all stay in the front 4 places. The treble, after dodging 3-4 up, takes the place of 5th place bell on the front, until the half lead; after that it takes the place of 6th place bell. The plain course is 96 changes but it doesn't contain every change 4 times, because the treble doesn't ring the same number of times in each place. An unnamed method with a similar structure extended to have double symmetry is this one. The plain course is 144 changes, containing each change 6 times.
The idea of taking a method in which 2, 3 and 4 stay in the front four places, and using the treble to fill in the work of other bells, can be applied to other methods than Bristol. Norwich Alliance is based on Norwich Surprise Minor. Warkworth Alliance is based on Warkworth Surprise Minor. This unnamed one is a bit like Bourne Surprise Minor.
Some other surprise major methods can be treated in this way. Here's one based on Rutland, in which the treble takes over the work of 7th place bell.