To summarize, you'll have to face four different problems :
1) The psychological problem.
Following a game, and suddenly discovering that it have been released as a brand new thing is always a little disturbing. Is this something new, or is this the continuation of what I already played ? Is the story the continuation of what I previously seen, or is it a new story ? Is this file including the previous parts or not ? Too many questions can come to mind when facing this situation.
Unless your story is really addicting, if you do it too often, you'll risk to face a loss of players. Having to do all the thinking and manipulations every now and then, why not. But having to do them every two/three updates, it's something different. We play for our pleasure, not because we want to pass few minutes preparing the game.
So, the "new game" thing must happen for a reason, like by example what was done with
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. The first game stopped when the said daughter came back to her original location. It's not just a new chapter of the story, it's a new volume of the series. Here the justification of the new game was strong, and even if it could have been seen as annoying by some, it was legit.
This being opposed to games that have a "new game" for random reasons,
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by example, or because the file size start to grow too much,
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by example. Don't take me wrong, both games are interesting despite their own flaws, but the need to start a new game every two (ES) updates or every five (DML) ones is the biggest of these flaws, and it will prevent these games to reach the level of support they could have expected at first.
2) The new player's pitfall.
If someone follow your game from the start, the fact that it is split in multiple games can at most be annoying, that's all. But you must also take in count that it's not everybody that will discover your game during its few first months of life. So, you need to think about what can happen to the players trying to join the folks after the end of the "first game".
These peoples will face at least two links. One labeled "last update" and one labeled something like "update 0.5". The one they'll download is obvious, it's the first one. The more advanced will be the story when they'll join, the less they will understand it. So, you'll need to do as authors do for books. Firstly the game will need to summarize what happened before. Secondly, you'll have to reintroduce every single significant characters and locations, in every one of your games ; a small introduction, but still you can't name the big bad boy of the game and expect for a new player to understand that there should be a very dramatic music playing in background.
It's great, it solve the problem of new players, but it create a problem for old ones. Have you ever read multiple volume of a book series in a row ? Aren't all these "previously in my series" and all these reintroduction of character annoying after some times ? Well, the exact same thing will happen to players following your game since a long time. So you'll have to choice. Either you don't really gain new players, or you'll slowly loss the old ones.
Some may argue that the new players just have to play the game from the start. Yeah, it's not false... The two games I named as counter example already have 3 different games both. Are you ready to download three games in a row just to play them ? Will you be still ready to download all the needed games in a row when they'll have 10 different ones ? It will end by being discouraging, right ?
3) The technical issues - save compatibility.
While it's not this difficult to do, it's also not this easy.
Basically speaking, each game share their save files with the previously released games. This can be done really easily by editing the "options.rpy" file and changing the value of "config.save_directory". Every games sharing the same value for this configuration variable, will use the exact same directory for their save files. Then, either you rely on persistent values, like
@79flavors said above, or you rely on the behavior of Ren'py to achieve the load of a save coming from another game.
Working with persistent values have its flaws. You'll have to discriminate your variables, some are needed locally for this game only, other will be needed in every single games. You'll have to prefix with "persistent." the one that need to be kept, will naming directly the other. How many times before you start to mix your thoughts and have a "whatever" variable and a "persistent.whatever" one, all supposed to be the same one ?
Relying on Ren'py's behavior is easier. You end your game in a label named, by example, "start_of_game_5", and you have the same label in the new game you created for the next update. Ren'py will load correctly the save file and you'll have access to all the saved variables. But there's a pitfall even with this method. The said "start_of_game_5" label must be big enough to ensure that player will effectively save inside it. Don't expect them to save when you'll display some kind of "save here" message on the screen. Too many games do this, and fail to be compatible when you'll play the next update. So, many players will save few interactions before this message. Usually it ensure the save compatibility, in this particular case, it can in fact break it because they'll be in a label unknown of the "new game".
4) The technical issues - the case of new players.
Alright, you've solved all the problems I talked about above. You'll start a "new game" only in relevant place of your story and don't do it too often. You've understood that the "continue with this label" solution is better than the persistent values one. This imply that you'll have a label name "start_of_game_5" which will be the start of this game for old players, and the regular "start" label for the new players. In this "start" label, you'll put a summary of the previous games, so players will not be lost in the story. You'll also set a flag that will include a short reintroduction of characters and locations, so the new players will really not be lost in the story.
In short, you think that you're ready... But you aren't.
What will happen if a player start your game at the third "new game" without wanting to play the previous ones ? After all, you did everything for this to be possible, because you don't want to force a new player to play the many previous games if he don't want to. So, you've a player aware of everything, that will understand enough to not be lost... but will also have no back history in the game. He have made no progress, he have made no choice. When the game will branch here or there, depending if he'd stole his roommate panties or not, you'll face a "no issue" situation because this player haven't stole the panties, but he also haven't not stole it.
This mean that you'll also have to generate this values when the game start. Here, the solution of facility is to generate an intermediary state for all the variables (inside the "start" label). But the problem is that it will force the player to have a given behavior. If he want to play the game as a good guy and you force the intermediary state for the bad guy path, you'll create inconstancy in the story. Things like "Hey, I know you pass your time to peek at me when I shower", followed by, "you're the nicest guy I know, not even looking at my panties when you had the occasion to do so".
The other solution is to make the player face theoretical situations. You'll ask him few questions like, "You've a crush on your roommate, one day, you found one of her panties in a place it shouldn't be. She surely have lost it, it will not miss her more if you take it. Will you take it ?". Then, you'll not just use the answer to define the value of a variable, but to determine the behavior of the player and so define many variables. By example, add a more direct question to this one. One that looks like, "When going to the bathroom to take your shower, you see your roommate panties on top of the laundry basket. Do you take it ?"
It the player answered "no" to both, he's a good guy, you'll set the variables according to this. If he answered "yes" to both, he's a bad guy, once again set the variables in consequence. If he answered "yes" to the first one, but "no" to the second, he's ready to perv, but fear the consequences. And it he answered "no" to the first one, but "yes" to the second, he's a full time perv ; the first panties didn't interested him, it was a clean one, but the second was touching her skin few minutes ago...
And voilà. You now know all what you needed to know about releasing a game in multiples parts (and not just multiples updates). As you can see, it's not impossible... but it imply way more works from the author to be done in an effective and reliable way that will not annoy the players.
