If you have had good experience from a contractor handling your occasional small moves with care and efficiency, they will probably be a natural contender when a large project arises. Nonetheless, a proper procurement procedure should still be followed (and indeed, the purchasing policy of the organisation will almost certainly dictate that there be a formal tender process).
A major commercial move is a truly critical project with the potential for extremely serious consequences if it is not carried out on time, without loss or damage. It is essential, therefore, to select a company with adequate resources, coupled with proven ability. Analyse their track record and performance, look for experience of your type of project in your industry sector and study their technical skills and knowledge. Ask for examples of previous projects similar to your own and take up those references at an early stage.
Your organisation may have its own format for formal tenders but often these are quite generic and do not reflect the specialist nature of removal work. Companies quoting will more than likely have their own proposal format. It can be helpful to lock this down by providing a list of headings against which their responses must be made, (see below). In this way you will ensure consistency of presentation and it will make it much easier to compare the responses, while being confident that they are all on a like-for-like basis.