tl;dr

If a woman suggests an open relationship, the conventional RedPill advice is to you should plate her and never consider a LTR with her. There is a slight possibility she's RedPill and is open to an unusual but mutually-beneficial relationship. Instead of rejecting the offer outright, you could test her suggestion to see if it's a good idea.

Background

Men and women are different. Women are the gatekeepers of sex, and men the gatekeepers of a relationship. Therefore, an equitable open relationship is asymmetrical, but similarly weighted on either end: the woman has many (emotional/validating) relationships with men, and the man has many sexual partners.

The following will go into some detail to give you a simple set of criteria to decide if the open relationship proposed is a good idea or a bad one. We start with the ideal "level 0" relationship, which is maximally beneficial for both the man (you) and the woman (your LTR).

LEVEL 0: The ideal Open Relationship for Both Partners

The woman has many orbiters who shower her with attention, gifts, and praise, and she provides them with emotional support, female advice, and sincere friendship. There is never any physical touch between her and her orbiters except the most cordial business-acceptable: a handshake, perhaps a momentary touch on the shoulder.

The man has many plates who give him full sexual access, and he reciprocates with complete sexual fulfillment for her, giving her orgasms, fulfilling her sexual fantasies, and in general, providing her exemplary sex. There is never a semblance of relationship: no emotional talks, advice, or monetary support.

All levels beyond this get closer to the broken status quo "open relationship" (aka "cucking") that is bad for all parties. Since people are complex animals, some can be quite happy on the higher levels, so I'll give their characteristics, on the off chance you need to understand them.

LEVEL 1 - Light Physical/Emotional Contact

The woman allows her orbiter some minor physical touch, such as an embrace or a slow dance. However, all touch immediately de-escalates. After a partner dance, for example, she and her orbiter immediately stop touching. After he hugs her upon meeting, they immediately part. At no point does her orbiter touch her in even the slightest sexual way without profuse apology and genuine effort not to repeat the mistake.

The man allows extremely minor relationship behaviour from his plate. He may occasionally pay for dinner or a cab ride, and occasionally listen to her most severe problems (such as after a plate is laid off or suffers a death in the family). All such emotional support quickly recedes to distance. The man never proactively offers emotional support to his plate.

LEVEL 2 - Intermediate Physical/Emotional Contact

The woman and her orbiter share some intimate touches. They may cuddle, and he may occasionally and mostly non-sexually touch her (fully-clothed) breasts or butt. At no point does this additional intimate touching tend toward sexual actions such as dry humping, heavy petting, etc. She and her orbiter perform no action that would be out-of-place in a family restaurant.

The man and his plate may have some more-lengthy or involved emotional attachment. Perhaps he will meet some of her family, and entertain regular (albeit minor) talks on problems in her life. He regularly pays for dates and occassionally allows her to come over to stay overnight. He occasionally will proactively offer to console her or give her emotional support.

LEVEL 3 - Open-Gates Physical/Emotional Contact

The woman and her orbiter/LTR have sexual contact. Anything from "dry humping" to a ginger two-fingered "hand job" all the way to full on screaming cowgirl riding his cock like a champion. At this point, she's opened the sexual gates. How wide she's opened the gate isn't particularly important.

The man and his plate/LTR have a full on relationship. She has moved in, and he and she spend hours talking about their relationship and lives. He's met her family, they have planned out a future together. As soon as the man is proactively building emotional rapport with the plate, she has become an LTR. He's opened the relationship gates, and how wide he opens them isn't terribly important.

Asymmetry Without Equal Weighting

If the relationship is to survive level 3, the assymetry must have equal weighting. That is, if your LTR has a full emotional/sexual relationship with an orbiter, and you don't have a full sexual/emotional relationship with a plate, then the relationship is dead, even if everyone wants it to be alive.

This is where today's "open relationship," as defined by the matriarchy, falls apart. The woman is out riding the cock carousel while the man is working two full-time jobs to pay the rent, the bills, and support her expensive lifestyle. Eventually this situation will come to and end, and it won't be any good for the man until it does.

If, in this unequally-weighted situation, your (ex-)LTR puts forth exceptional effort to bring you emotionally-stable plates to help even out the balance, then the relationship is still dead, but she's at least putting in good faith effort to revive it. I think a good rule of thumb is that she introduces you to at least 2 attractive potential plates per week that fully understand the relationship. Any less effort indicates not only is the relationship dead, but she clearly has no interest in reviving it.

By the same measure, if you're engaging a plate on a full emotional/physical relationship, and your LTR is not, then you are obligated either to close the relationship or help her bring attractive orbiters into the fold.

Lesson Learned

Using this guide, you can test if your LTR really wants an unusual but mutually-beneficial open relationship. If there are doubts, follow the tried-and-true RedPill advice: plate her and never consider her for an LTR ever again.