Just throwing random ideas out there
1) some VNs have a thing where you have to pick who you romance at the beginning of the game and then you play their story which only briefly coincides with other stories. Generally it is thought a poor way to handle it, but having a couple chapters/parts where they can't romance anyone but get to know them, may help, and then play out their story.
2) Picking just (romance) worked pretty well for Loren and other things like Mass Effect. A strong story and recognition of the romance in dialogue will usually make up for a lack of other things like serious romance mechanics.
3) When having more than one character, you have a finite amount of points to "level" a relationship. Choosing which one, and who gets it will be harder since at least one person will have to be alone. And get a bad ending??
4) With a rival system, where not passing skill checks at certain points mean they go to the other person instead of you. The "heart Meter" could be converted to a your rivalry with another character. In the first Heileen there is a bit of this with the Lesbian option where she feels you are competeing for affections of the guy she likes. Here, a rival could be a friend or not. And the stats you build will be checked at different times and if you lose they gain affection, and if you win you gain affection. This works more in a court espionage game.
5) In a game not about romance, using romance options may eat up skills, so that it actually hurts your chances of doing something else. Also incenticises not going after anyone as a logical way to play. Some free dating games do this even casually with not knowing what someone wants and buying them gifts or spending money on dates. But could be done as a more invested way by not only costing money (which then demands a job) but in other ways such as eating into an important part of the schedule, missing a day, getting demoted, losing a connection. It is an erroneous idea you can't have a "career" and family but a game that really makes one eat into the other may be fun.
6) Ask the player wants to be dating a man or a woman, and then write from someone already with them. It is said that only will they won't they are good, but very few stories are about a couple already together. (Not counting ones where there is no romance but rescue significant other is the plot) The romance will be recognized but in a different way. You would have to write to make up for the romances presence, but only 4 romances *shrug*
7) Don't have exactly, romantic choices, but have the characters talk to one another and after so many chats, the character comes on to the player (based on personality maybe? so Draco liked funny guys, but Loren "hated" them) and so they are pursuing the MC (which is what is being done anyway on a meta level anyway from your standpoint) and the MC can start something, deny them, or have a 3rd, I don't know option. Players aren't used to being pursued game mechanics wise so they will either love it or hate it, or you can choose at the very end as well. Most romances actually aren't really romances until a certain point anyway.
Hope that helps, sorry it it became long