Nothing is wrong with doing so IMO. Do they know you will have a parallel project of your own? Have they said that's fine with them? If so, it would be best to revise the contract to reflect that. Sometimes the initial contract they propose is just boilerplate from their files that they always use with consultants and not really specific to this engagement. But if things unexpectedly come apart later on, the lawyers look back to what is in the contract, not to informal understandings that were never included. You should not have informal understandings that are at variance with the contract.
Perhaps useful (Google results): https://research.uiowa.edu/uirf/pages/universal/forms-and-sample-agreements.html http://contracts.onecle.com/type/32.shtml http://www.stemcellnetwork.ca/uploads/File/resources/template-License-Agreement-eng.pdf http://www.openinventionnetwork.com/pat_license_agreement.php http://www.inventioncity.com/invention-licensing-agreement-example.html http://ilicensemusic.com/license
there has been very good general legal advice on this thread. The distinction between licensing and ownership was a fantastic practical point for a code developer getting into contractual relationships. It obvious came from someone with a very good understanding or a good deal of experience.