Hello Lea.
You asked him to originally come up with three design schemes, which you then selected and chose to go forward to planning with the third (bungalow). Now you would like to make changes to the drawings for the bungalow for which you had planning approved, is that right ?
Usually there are two sets of drawings invloved in such a project. Planning and Construction drawings.
Given you have planning permission, it depends on what stage the engineer is at with the construction drawings.
If the construction drawings are completed then from the engineer's point of view, amendments are being made against a completed stage and he could argue that they are extra charges.
If they are work in progress it is completely within your scope to ask for amendments. However the type of amendments you want also has a bearing. you probably would not be able to change anything structural, windows, levels etc without re applying for planning permission. Anything internal layout etc, should be ok.
Check with your local council planning department as to the position on the level change and what your options are, before you make any decision.
An engineer or architect should only bill you in stages and this will normally be agreed at the initial contract. So hopefully you have only paid for the planning application stage (although 20k is a helluva lot for this) and maybe construction drawings stage at this point.
If you have not paid anything towards the project supervision stage, then failing any reasonable outcome in your negociations with him, seriously consider firing him and engage a new engineer to complete the project.
If you continue down the line with him, you will most likely run into further troubles. You will also have doubts about his committment to your project.
Consider getting advice from an independent consulting engineer as to your best option forwards.
AndyH
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