i assume when you say solvent weld that you are referring to plastic waste pipes - so if you are asking whether or not you can mix welds, push fit and compression fittings on waste then the answer is not always.
if you are referring to your plumbing then no i dont think that solvent connectors are available for plastic plumbing yet, push fit and compression only.
32 and 40mm waste pipes can be joined with compression fittings as well as either solven weld or push fit but you will find that in a lot of cases the pipe thickness varies beteen some pipes depending on where you buy the, If the solvent fitting flaps about on the pipe its usually because the pipe comes from a DIY shed and is designed for their push fit fittings. Solvent weld fittings shoul;d be tight on the pipe before the weld is applied.
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