I'll give two ideas, but mind you, I lack modding experience ;)
First idea is to make it possible to nominate as co-emperor any of your immediate family - brothers, father, your sons and their children, without consideration of the current heir apparent to the Empire. And also, in case of regency, the acting regent, even if he/she is not the current heir, to be able to receive the title. Not authomatically of course, many regents were never invested as co-rulers of the Empire. Let's say if particulary ambitious and resourcefull regent rule long enough, he can receive the opportunity through an event or could start a plot with plot decision if he gain enough support. It's more like filling the rare occasions in Byzantine history that such things happened.
The second idea, much more easy to implement I hope, is to make the mechanic usable not only for the Byzantine empire, but for others too. Most of the european monarchies had such systems, but my suggestion is based on the fact how much influence the empire had on her neighbours, namely the Second Bulgarian Empire and the Serbian Kingdom. I'm not so sure for Serbia, although their first(and last) Tsar Stefan Dushan was indeed a "Mlad Kral"/Junior Rex in the reign of his father, before ascending to the throne. For the bulgarians, dual rulership existed since the liberation from byzantine rule - the first rulers of Asen dynasty Ivan and Petar ruled together. Hard to say if it was the byzantine influence, but in later years the tsars invested their sons as junior rulers, giving them parts of their domain to rule.

Partly, the regent thing already exists in the base ck2 as one of the regent plots (usurp throne). As for the others, it seems reasonable to add close kinship coemperor part, but well... I have to come up with some mechanics that differentiate non-heir emperors with base game despot title, which is also only awardable to the emperor's close kins (that is a reminiscence of Paradox implementing the coemperor concept, imo). Hmm, maybe I could make coemperor appointment gives him strong claims to the empire, but without the usual opinion panalties. As for the other kingdoms part, I think it is a great idea! It is indeed true that many European monarchs appointed their son as co-rulers in order to promote his legitimacy, and prevent turmoils in case of his early death. How do you think about allowing other kingdoms to appoint co-rulers if they reach imperial administration (a reflection of adopting the Byzantine influence)? Stephen Dushan died 1355 (a fairly late-game).

Also, please note that I, as the modder, also have to think about the game balance. If the symbasileus appointment is entirely up to the emperor, that would partly nullify the imperial election system in the base game, and degrade it to the heir appointment system used by Buddhists in the base game. There are people who denounce overpowered mods, and I need to consider their opinions too. But that does not means your idea is bad. I think it is a great inspiration! If you have any ideas to overcome this conflict of interest (as you now know the backgrounds of my decisions for this mod), please share them to me. P.S. I really appreciate your approval and compliment. That's what gives the modders a strength!

The most basic solution for not OP the title I can think of is to give a char modifier to the giver with negative prestige per month, like -0.10 and one time prestige hit like -50 or -100 if the chosen co-emperor isn't "suitable" for the office - children or women. Or with different, harsher numbers. Could use more variables, a more sophisticated system, that checks traits/attributes/modifiers/religion etc. And another suggestion that I think is historically accurate - maimed, and generally lacking body parts characters to be automatically excluded as possible co-emperors.

For other realms to adopt the mechanics - well, PDX never tried to simulate that part of byzantine influence and politics in the region for a reason :) My suggestion is to give the holder of k_serbia and k_bulgaria titles if their prim title is empire other than Byzantium and HRE, they are feudal and are of the south slavic culture group, following orthodox christianity(or a dominant heresy) the mechanic of appointing co-emperors.

I have updated the mod to include features that were inspired by your suggestions, @finrod. Also, partly inspired by this conversation, I am aiming to introduce some feature that allows factions that demand installation of someone to the co-emperor title, which will occur much more often when the empire is at regency (So, if the regent is a claimant and ambitious, he will certainly accept any ultimatum that makes himself a symbasileus). I have yet to implement the other empires' co-emperor feature partly because some part of the code heavily depends on the uniqueness of the byzantine and roman empire titles.

About HIP's compatibility mentioned in the comments, I think you need to make a separate mod or a compatibility patch. HIP modifies "01_succession_voting_specials.txt", so you need to merge your changes to the HIP version of the file. And of course the mod requires the appropriate dependency setting in order to make sure that you override HIP's file. It seems to work just fine after doing these changes.