Every transposition event is theoretically random (but some transposons have preferred integration sites) if the transposon is activated from the plasmid, it should integrate at a different site in the chromosome, most of the time. so a transposon can be used multiple times theoretically.

Practical difficulties

each transposition event is selected commonly using antibiotics, this limits multiple usage of transposons,

further, there is a possibility of the transposon recombining with earlier transposon insert.

The usage of suicide vectors to deliver transposons ensures that there is one transposition event in a cell. if the same transposon is used multiple times, it would activate the earlier transposon also leading to multiple uncontrolled transpositions, increasing complexity.

given these difficulties it is not preferable to use a transposon multiple times in the same cell, for most purposes.

I definitely second Vamsi's very good answer answer. Even with a suicide plasmid, you usually still get some colonies with multiple insertions into the same genome due to some cells receiving the plasmid multiple times. When we want to do further work with a transposon mutant it's usually verified to only have one copy of the transposon by qPCR or Southern blotting for this reason. Typically multiple rounds of transposition are only done with different transposons, ie. if you used a Mariner transposon then a Tn5 transposon, as these have different recognition sites and aren't likely to interact with each other.

The only real use I could see for a transposon in a replicative plasmid would be if you want to induce huge genomic rearrangements/deletions for whatever reason.

@Alexandra Johnson

Yes.

As like you said that "huge genomic rearrangement/deletions" at the end of your answer, what I want to do with traposons is to generate genome-wide continuous mutagenesis

@Vamsi Bharadwaj SV

@Alexandra Johnson

I think if I introduced single copy of transposon (cut-and-paste) and induced expression of cognate transposase, multiple and continuous transpositions of the single transposon could be occur inside the E. coli.

I expect that the single transposon repeatedly inserted in and excised from the same genome with the activity of cognate transposaes.

Unfortunately, I cannot find some references about whether continuous transpositions could be or not.

Have you ever seen the occurrence of this event in vitro or in vivo?