How to model the probability of a truth claim given an arrangement of eyewitness accounts supporting specific instances of that claim? Note: the title is adapted from my Philosophy.SE question Epistemic value of multiple eyewitness accounts: single event vs. multiple events given a fixed number of eyewitnesses?. See meta discussion here.

Intuitively speaking, multiple independent eyewitness accounts of a single event are more convincing than a single eyewitness account. For example, multiple independent eyewitness accounts of a loud explosion in a remote area (e.g. from different locations and viewpoints) are more convincing/reliable than a single account (e.g. maybe the single witness hallucinated the explosion).
A bit more formally, if we define X as some truth claim about some event, process or phenomenon in the real world, we could say that:
P(X is true | multiple eyewitness accounts) > P(X is true | a single eyewitness account)
However, what happens if we keep the number of eyewitness accounts constant and only change the number of events?
For example, let X = "alien abductions are real", and let Ei be a concrete example of an (alleged) alien abduction. X is a general claim, Ei is a claim about a very specific instance of X. It is clear that Ei entails X. Thus, which of the following probabilities is greater than the others?

*

*P(E1 is true | N eyewitness accounts for E1)

*P(E1 is true or E2 is true or ... or EN is true | one eyewitness account for Ei, for each i in {1, ..., N})

*P(E1 is true or E2 is true or ... or EN/2  is true | two eyewitness accounts for Ei, for each i in {1, ..., N/2})

*P(E1 is true  or E2 is true or ... or EN/3 is true | three eyewitness accounts for Ei, for each i in {1, ..., N/3})

*Etc.

In other words, given N eyewitness accounts, what is the optimal distribution of eyewitnesses over specific alleged instances of X that maximizes the probability of X being true? What should be more convincing, 1000 eyewitness accounts for E1, 500 eyewitness accounts for E1 + 500 eyewitness accounts for E2, etc.?
Notice that I used eyewitness reports of abductions by aliens as an illustrative example, but the reasoning can be extended to other rare events, such as reports of miracles, paranormal phenomena, angelic encounters, Bigfoot sightings, testimonials from whistleblowers (conspiracy theories), etc.

TL;DR
The paper Holder, Hume on Miracles: Bayesian Interpretation, Multiple Testimony, and the Existence of God deals with Bayesian updating based on witness reports from multiple events. Holder only considers the case of two events, so I will adapt his calculations to the general case.
I expected, intuitively, that (other things being equal) a single event reported by 100 witnesses has a higher posterior than 100 events reported by a single witness each. This is not what happens in general. The picture is more complicated and the answer depends on a certain inequality between the reliability of witnesses and the Bayesian prior. When there are sufficiently many reports, the witnesses are reasonably reliable and the prior is very low (as with alien abductions and miracles) the all-in-one distribution of testimonies over events is better, but with less reliable witnesses and/or higher priors this reverses. It looks like for large $n$ the posteriors of intermediate distributions line up in between the all-in-one and one-in-all, but I did not study this closely.
Assumptions
I assume that all events $E_i$ are equally probable and independent with the prior probability $p=p(E_i)$. Each one is reported by one or more witnesses, and the testimonies are denoted $T_j$. I also assume that the testimonies are independent of each other and of events they are not testimonies for.
Single event
When there is a single event $E$ and a single testimony $T$ the probability is updated according to the standard formula
$$p':=p(E\mid T)=\frac1{1+\frac{p(E^c)}{p(E)}\cdot\frac{p(T\mid E^c)}{p(T\mid E)}}=\frac1{1+\frac{1-p}{p}\cdot\frac{p(T\mid E^c)}{p(T\mid E)}}.$$
Let us denote $a:=\frac{p(E^c)}{p(E)}=\frac{1-p}{p}$, the prior odds against the event, and $r:=\frac{p(T\mid E^c)}{p(T\mid E)}$ the ratio of witness's reliability (or rather unreliability): if $r>1$ then the witness is more likely to report the event if it did not happen than if it did. By simple calculation, $a':=\frac{1-p'}{p'}=ar$ are the updated odds against. So after $n$ updates (based on independent testimonies with identical statistical characteristics) we get $a^{(n)}=ar^n$ and
$$p^{(n)}=\frac1{1+ar^n}.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \text{(1)}$$
Note that for unreliable witnesses ($r>1$) this posterior decreases rather than grows with $n$, converging to $0$ when $n\to\infty$. This is because for $r>1$ their reporting actually makes the event less likely.
Multiple events
Following Holder, the probability we are looking for here is $p(E_1\cup\dots\cup E_m\mid T_1,\dots,T_n)$ — that at least one of the reported events happened. This is not the probability of $X$ conditioned on $T_j$, but the leftover probability (of $X$ without any confirming events) is the same whether we are updating based on one or multiple events. So comparing to $p(E\mid T_1,\dots,T_n)$ gets us what we want.
By the complement rule, and taking into account independence of $E_i$:
$$p(E_1\cup\dots\cup E_m\mid T_1,\dots,T_n)=1-\prod_{i=1}^mp(E_i^c\mid T_1,\dots,T_n).$$
Suppose we have $n_1$ testimonies for $E_1$, $n_2$ for $E_2$, and so on, $n=n_1+\dots+n_m$. Assuming again that all statistical characteristics are identical, and each testimony influences the probability of its event only, we have
$$p(E_1\cup\dots\cup E_m\mid T_1,\dots,T_n)
=1-\prod_{i=1}^m(1-p^{(n_i)})\\
=1-\frac{a^mr^n}{\prod_{i=1}^m(1+ar^{n_i})}.\ \ \ \ \ \ \ \ \ \ \text{(2)}$$
When $m=1,n_1=n$ we recover the single event formula.
Comparison
Since comparing posteriors across the full range of $m,n,a,r$ looks hairy I will restrict to the extreme cases, $m=1$, $m=n$ (single event reported by $n$ witnesses, and $n$ events reported by a single witness each), and consider only the case of large $n$, which is arguably where the results become meaningful. The posterior for the latter reduces to
$$\widetilde{p}^{(n)}
=1-\left(\frac{ar}{1+ar}\right)^n.\ \ \ \ \ \ \ \ \ \ \text{(3)}$$
In contrast to $p^{(n)}$, this posterior converges to $1$ for any values of $a,r>0$, even when the witnesses are unreliable with $r>1$. This already tells us that for large $n$ this posterior is closer to $1$ when $r>1$.
When $r<1$, we have from calculus that $p^{(n)}=\frac1{1+ar^n}\sim1-ar^n$ for large $n$, so which one of $(1),\ (3)$ is larger for large $n$ is determined by the direction of the inequality between the bases of the exponents, $r$ and $\frac{ar}{1+ar}$. In particular, for $p^{(n)}$ to dominate we need $a(1-r)>1$. This will be the case if the prior odds against our events are high ($a\gg1$, which is, presumably, the case for alien abductions and miracles), and the witnesses favor what actually happened ($r\ll1$).
Discussion
In the case of multiple events with single reports even anti-witnesses (with $r>1$), who drove the probability down to $0$ for a single event, will now drive it up to $1$. This is simply the consequence of the independence of $E_i$ and the fact that even anti-witnesses leave the posterior of each event positive. Looking at $(2)$, it seems that the all-in-one and one-in-all distributions are the optimal ones for large $n$ (due to exponential dichotomy), but I did not prove this rigorously. One has the maximal posterior (other things being equal), the other the minimal, and the rest line up in between. Which is which is determined by the inequality $a(1-r)>1$.
Independence across the board is assumed above to make the calculations tractable, and is not  realistic. For example, Holder calls assuming independence of $E_i$ "too simplistic" because "if we know that one miracle has occurred then our reasoning to the intrinsic improbability of miracles in general is wrong, and we should instead assume that they are likely". Assuming dependence will reduce the posterior for multiple events because each will contribute less to it, so in conditions that make all-in-one distribution optimal it will remain so. However, interdependence of testimonies for the same event is also more than likely, and would reduce that posterior. How all of this balances out in the end depends on how these dependencies are quantified, which is hard for me to guess.
Another confounding factor is evidence against. For example, from testimonies that confirm the validity of natural laws (in case of miracles) or debunk alleged encounters (in case of alien abductions). I suppose some of that goes into the inscrutable prior, but the quantitative effect on the posterior is hard to assess. I suspect it is a large part of why miracles and alien abductions are not widely believed despite the posteriors approaching $1$ for large $n$.
