This is simple enough not to absolutely require cutandpaste reprex
(see the FAQ, but it's a good idea to cut friction as much as possible.
This is a concise way to do this, with little syntax to master. I'll unpack it below
# fake data created by random sampling
# without a seed, so they are likely to
# be all different and different each
# time data frame is created with this
# snippet
m < matrix(
c(plate = 1:50,
sample(20:100,50, replace = TRUE),
sample(20:100,50, replace = TRUE),
sample(20:100,50, replace = TRUE)),
nrow = 50,
ncol = 4
)
colnames(m) < c("plate","m1","m2","m3")
head(m)
#> plate m1 m2 m3
#> [1,] 1 32 72 51
#> [2,] 2 47 60 89
#> [3,] 3 53 84 23
#> [4,] 4 94 98 78
#> [5,] 5 50 72 100
#> [6,] 6 98 61 47
mark_na < function(x) ifelse(x < 60,NA,x)
m[,2:4] < apply(m[,2:4],2,mark_na)
head(m)
#> plate m1 m2 m3
#> [1,] 1 NA 72 NA
#> [2,] 2 NA 60 89
#> [3,] 3 NA 84 NA
#> [4,] 4 94 98 78
#> [5,] 5 NA 72 100
#> [6,] 6 98 61 NA
^{Created on 20230405 with reprex v2.0.2}

My paradigm of using
R
is school algebra—f(x)=y. x is an object that needs some transformation, y is the object containing the transformation and f is the function object that does the transformation. Each of these may be, and usually is, composite. 
The object chosen for x has a big influence on f. I've used a
matrix
because all the contents to be subject to f is numeric. Amatrix
must be either all character or all numeric. Internally, both columns and rows are vectors. Adata frame
, which is where incoming data usually lands, can mix character and numeric types. *However, both columns and rows are lists. This is an important difference because a matrix can be treated as a single object and transformed more simply. 
The function isolates the logical condition to be tested—whether a value is less than 61, because those are the values to be replaced with
NA
. 
The
matrix
object,m
, has objects and rows. Herem[,2:4]
means all rows ofm
(because therow
position in the brackets is empty and columns 2:4 (if we wanted only the second and fourth column, it would bem[,c(2,4)]
). Think row/column, row/column. If only dealing with columns, it can be shorthandedm[2:3]
which we usually do. When we want to change only some rows, it would be `m[1:7,2:3]. I find it helpful to always have the comma—one less thing to keep track of. 
At this point, we know that we are changing every thing in
m
except the first,plate
column with a value of less than 61 toNA
and we know how. Now, we do that in a single pass by applying our function to the target columns by columns (we could also do it rowwise). That's whatapply
does. 
As far as variable dimensions,
dim()
works like the subset operator, row/column.m
is
> dim(m)
[1] 50 4
The script will work for any numbers of rows. Some wand waving is required for a variable number of columns. Come back with a reprex
if you need help with that case.