R Under development (unstable) (2023-12-07 r85661 ucrt) -- "Unsuffered Consequences"
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> library(bbmle)
Loading required package: stats4
> 
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> d <- data.frame(x,y)
> oldopts <- options(warn=-1,digits=3)  ## ignore warnings
> m1 <- mle2(y~dpois(lambda=ymax/(1+x/xhalf)),
+            start=list(ymax=1,xhalf=1),data=d)
> m1

Call:
mle2(minuslogl = y ~ dpois(lambda = ymax/(1 + x/xhalf)), start = list(ymax = 1, 
    xhalf = 1), data = d)

Coefficients:
 ymax xhalf 
24.99  3.06 

Log-likelihood: -28.6 
> y2 <- c(26, 17, 10, 15, 20, 5, 9, 8, 5, 4, 8)
> d2 <- data.frame(x,y=y2)
> 
> m2 <- update(m1,data=d2)
> m2

Call:
mle2(minuslogl = y ~ dpois(lambda = ymax/(1 + x/xhalf)), start = list(
    ymax = 1, xhalf = 1), data = ..1, lower = -Inf, upper = Inf, 
    control = list())

Coefficients:
 ymax xhalf 
24.63  3.16 

Log-likelihood: -29.6 
> m3 <- update(m1,.~dpois(lambda=c),start=list(c=5))
> m3

Call:
mle2(minuslogl = y ~ dpois(lambda = c), start = ..2, data = list(
    x = 0:10, y = c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)), lower = -Inf, 
    upper = Inf, control = list())

Coefficients:
   c 
11.5 

Log-likelihood: -42.7 
> options(oldopts)
> 
> proc.time()
   user  system elapsed 
   1.39    0.04    1.42