Here are a bunch of different possible competition phases for solo skaters. If there's interest, I could make a list for couples or group disciplines as well.
Can you think of other examples?
Which of these could be worthy of a championship as stand-alone events? Which two or three events could best be combined into a multi-phase championship comparable to the current short and long programs?
Which could be appropriate for male and female skaters to compete in the same event?
Which could be appropriate as ISU-sponsored events but not appropriate for Olympic competition?
Which would be of interest to some skaters or some audiences but not appropriate for the ISU to sponsor at all?
Traditional programs to music
The scoring of any of these could have an explicit emphasis on either the technical content or the overall performance qualities or balance between them, or the weighting between them could be left up to each judge to determine, or the system can be built to reward whatever each skater does best without preconception as to which categories of skills are more valuable.
* Completely free program: Show us all your best skills that you can fit into 4-5 minutes, to music of your choice, no restrictions or requirements, maybe a few illegal types of moves (pre-1982 freeskate rules)
* Well-balanced free program: Show us all your best skills that you can fit into 4-4.5 minutes, to music of your choice, with required elements and restrictions on repeated skills and quantity of each kind of element to ensure "balance" but except for a few forbidden non-skating-based moves almost anything is allowed either within or between element slots (IJS era freeskate rules)
* Freer well-balanced free program: Somewhere between the above extremes, with a few restrictions, requirements, and/or guidelines (early 2000s well-balanced freeskate rules, or fewer restrictions in 1980s and 90s); some flexibility in choosing number of elements from each category if judged by IJS
* Compulsory long program: Standardized longer program that requires all skills expected at that level, with some flexibility to add more revolutions to jumps, more variations to basic steps, spins, entries and exits of elements, transitions, etc., to demonstrate additional skills
* Compulsory short program: Standardized prechoreographed program in which everyone does the same steps and same element layout, to the same music if applicable, with variations only in rotational direction or number of revolutions where applicable; specific elements and choreography change each year (like compulsory dances, or gymnastics compulsory routines of the past)
* Standardized shorter program in which everyone must do the same very specific required elements expected of all skaters at that level, but music and choreography including modest variations of the elements are at each skater's discretion; specific elements rotate each year
* Shorter program in which everyone must do the same required elements representing a subset of what is expected of all skaters at that level, but music and choreography including modest variations of the elements are at each skater's discretion; specific elements rotate each year; some elements allow for choices within the definition of the element including some jump takeoffs or number of rotations, specific steps or spin positions (short programs 1973-88, and junior short programs mid-1990s to present)
* Shorter program in which skaters must fill the same general categories of elements but most variations that fit the category and required number of jump revolutions are allowed (senior short programs 1989 to present)
Technical competition phases without music, judged on difficulty, quality, technical correctness only:
* Compulsory technical program requiring selected specific moves or categories of moves expected of all skaters at that level, with some flexibility to add difficulty; individual transitions allowed and considered; no music, judged on technical merit only
* Compulsory program for jumps and separate compulsory program for spins requiring certain categories of jumps/spins with flexibility to showcase your own best difficulty or variations; no music, judged on technical merit only
* Jump contest in which skaters must execute required jumps one at a time in a required sequence, two tries for each, with elimination after failing to execute any element along the way (Top Jump format from the late 1990s)
* Element competitions (jumps, spins, school figures or prechoreographed stroking/step sequences) in which the required elements are executed one at a time and each scored separately, with a combined total score for the whole competition category (e.g., school figures as practiced as an initial competition phase up to 1990 and as a separate discipline in the 1990s and rarely beyond; some spin, jump, or Moves in the Field competitions held at local competitions mostly at lower levels) -- spin features, jump takeoffs and numbers of revolutions, variations to add difficulty may or may not be allowed and rewarded
Competition phases focused on use of basic skating skills to express musical rhythms and styles:
*Solo original set pattern dance: Musical rhythm/tempo/theme specified each year; each skater/team creates their own pattern that must progress continuously around the perimeter of the rink and must be repeated for a total of 2 or 3 patterns; no jumps, spins, lifts, etc., allowed -- IJS levels for the pattern as a whole or broken into 2-4 segments?
*Solo original dance: Musical rhythm and theme or selection of related themes specified each year; some specified elements (with levels under IJS as applicable) and restrictions on other types of elements allowed; may also include some requirements for pattern layout
*Solo short dance: Musical rhythm and theme or selection of related themes specified each year; some specified elements, including a prechoreographed pattern dance in which everyone skates the same steps in the same narrow allowed tempo range and also including several additional required elements (with levels applicable) and restrictions on other types of elements allowed
*Footwork program: Music selection entirely at the skater's discretion; elements such as step sequence of a specified shape, leveled spiral sequence, field moves sequence (with defined requirements and level features), twizzle sequence, school figure variations -- specific elements may be required every year or may rotate, or skaters may have an option of choosing any 3-4 elements, perhaps with 1 step sequence required
Artistic programs, in which the scoring may give the highest weight to fundamental skating skills or to overall aesthetic impact:
*Artistic freestyle program, any kind of music, limited number of freeskating elements of the skater's choice (e.g., 3-4 jump elements with at most one combination, 2-4 spins allowed in a 3- to 4-minute program), judged on both TES and PCS but weighted to give precedence to PCS
*Solo free dance with specific required/allowed elements for points and levels but no multirevolution jumps or overhead lifts allowed (and maybe restricted spins?); music should have identifiable rhythm; PCS weighted to balance the TES
*Completely free program, with a wide allowed time range, in which any type of music and any type of elements are allowed; hand props, costume changes, etc. allowed; judged on PCS only
*Completely free program, with a wide allowed time range, in which any type of music and any type of elements are allowed; hand props, costume changes, etc. allowed; judged by audience response