It's fair to say that when a closed group admits another, it is (at least transiently) no longer closed. From a medical perspective, there is risk assessment and risk management that should be part of the decision making and planning. While there is little evidence that swingers are more likely carriers of a sexually transmitted infection than persons who report monogamy, STIs are known in both groups. There are five general groups of STIs worth considering:
1. Common, very easily transmitted, easily detected, easily treated. Chlamydia and Trichomonas are examples in this group. Transmission rates from a single sexual contact with those untreated and shedding the organisms are very high.
2. Common, very easily transmitted, easily detected, must be identified early and treated aggressively to prevent serious health issues. Gonorrhea and Syphilis are examples in this group. Same story--a single contact with an infected person who is shedding pathogen is very high.
3. Somewhat common, transmissibility moderate, often detected late, curable but costly to cure, no preventive immunization is available. Hepatitis C is in this group.
4. Less common, less easily transmitted, often detected late, chronic and must be managed with suppressive treatment. Herpes and HIV fall into this group. The former is a nuisance, the latter requires care forever to suppress the viral load. (Side note, those with HIV who responsibly use their meds and suppress their viral load to undetectable are highly unlikely to transmit the illness to partners/playmates. )
5. Less common, transmissibility harder to assess, often detected late, chronic, for which preventive immunization is available. HPV and Hepatitis B fall into this group.
All of the above is invites closed groups "adding" a single or a couple or whatever to stop, think, assess, and decide how they want to proceed. There are two major considerations.
1. Are all members of the (currently) closed group free of these pathogens? Are the proposed new entrants similarly free of these pathogens? Those considerations suggest adding members should prompt _all_ members, current and proposed new ones, to simultaneously test.
2. What is the probability that the group is actually remaining 'closed'? The larger a group gets, the lower the probability that the group is actually remaining closed.
It's worth taking 30 seconds to read this article in New Scientist: https://www.newscientist.com/article/dn913-six-degrees-of-copulation The salient quote from the brief piece:
By checking how many sexual partners people had in one year, they could estimate the number of sexual liaisons needed to link two people. “We found it could be much less than six,” says Amaral. “Any two people might only be two or three connections apart,” he says. “Those people who think they are in no way connected to those with STDs are very wrong.”
(Disclosure: One of us was a peer-reviewer of the original publication in Nature, an archived form of which can be found here: https://arxiv.org/pdf/cond-mat/0106507 )