Can I increase the standard deviation of a series without increasing its mean?

Question

I have a series of values. Can I modify them in a consistent manner such that it's mean remain the same but standard deviation increase by 1? 1 is just arbitrary in this example

Answer 1

You can insert mean $\pm c$ which won't change the mean but will change the variance by a calculatable amount in terms of $c$ and the original population size.

Note this only works on probability distributions on finite sets.

Answer 2

If $\mu$ denotes the mean and $\sigma$ the standard deviation then replace value $x$ by value: $$(1+\frac1{\sigma})(x-\mu)+\mu$$

The new mean will be $\mu$ and the new standard deviation will be: $(1+\frac1{\sigma})\sigma=\sigma+1$.