Tom,

Yes, you can.  You can adjust the Acquisition Value to account for the cost of the additional improvement to the asset.  This can be done in the same way as you would handle it if a tardy invoice came to your attention, and you realized that the Acquisition Value was understated.

If you do this, you will change a critical field.   You will see a warning first, followed by a dialog box enabling you to choose the effective date of the change.  I recommend you go with the default, i.e., the Current Thru Date, in this case.  Then, you will need to apply your book defaults in order to overwrite all open books with the new acquisition value.

This will put the asset into an under-depreciated state -- important if you are a straight-line depreciation method for financial reporting.  If you are not clear on how your company is handling under-depreciated assets, I recommend you change this method to RV in your Internal Book.  Again, you will see the warning, followed by the dialog box, and again, you will elect the default Current Thru Date.  

If you change the method to RV, the estimated life may likely change too.  This is done automatically by the heuristics built into the program.  If you see the value change, you will want to change it back to the estimated life you were using before the change.

I have provided you with the answer to the question you asked without really knowing what type of improvement you have made.  There is another way to handle it, Tom.  

Create a new asset to account for the additional improvement instead.  It will have a different placed in service date from the original asset.  But the values for the property type, estimated life, and depreciation method will all be the same.

Next, you will want to tie this new asset record to the original record in some way.  Consider adding a note or putting a special code into the description field on both assets -- something that will serve you as a way of marrying the two at a later date.  This can be very helpful in the event of a disposition where you need to find both asset records and dispose them at the same time.  

But having a separate asset record for the additional improvement now gives you the flexibility to dispose it separately from the original asset.  Thus, if you think there is any chance that the additional improvement might ever be removed from the original asset and used, e.g., after the original is disposed, you may want to go with this alternative way of accounting for the addition.